RD Sharma Class 9 solutions Chapter 17 Constructions

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RD Sharma Class 9 solutions Chapter 17 Constructions

RD Sharma Solutions Class 9 Chapter 17 Constructions Ex 17.1

Question 1.
Find the area of a triangle whose sides are respectively 150 cm, 120 cm and 200 cm.
Solution:
Sides of triangle are 120 cm, 150 cm, 200 cm
RD Sharma Class 9 Chapter 17 Constructions

Question 2.
Find the area of a triangle whose sides are 9 cm, 12 cm and 15 cm.
Solution:
Sides of a triangle are 9 cpi, 12 cm, 15 cm
RD Sharma Class 9 Solutions Chapter 17 Constructions
RD Sharma Solutions Class 9 Chapter 17 Constructions

Question 3.
Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.
Solution:
Perimeter of a triangle = 42 cm
Two sides are 18 cm and 10 cm
Third side = 42 – (18 + 10)
= 42 – 28 = 14 cm
RD Sharma Class 9 PDF Chapter 17 Constructions

Question 4.
In a ∆ABC, AB = 15 cm, BC = 13 cm and AC = 14 cm. Find the area of ∆ABC and hence its altitude on AC.
Solution:
Sides of triangle ABC are AB = 15 cm, BC = 13 cm, AC = 14 cm
Constructions Class 9 RD Sharma Solutions
RD Sharma Class 9 Solution Chapter 17 Constructions

Question 5.
The perimeter of a triangular field is 540 m and its sides are in the ratio 25 : 17 : 12. Find the area of the triangle. [NCERT]
Solution:
Perimeter of a triangle = 540 m
Ratio in sides = 25 : 17 : 12
Sum of ratios = 25 + 17 + 12 = 54
Class 9 RD Sharma Solutions Chapter 17 Constructions

Question 6.
The perimeter of a triangle is 300 m. If its sides are in the ratio 3:5:7. Find the area of the triangle. [NCERT]
Solution:
Perimeter of a triangle = 300 m
Ratio in the sides = 3 : 5 : 7
∴ Sum of ratios = 3 + 5 + 7= 15
Class 9 Maths Chapter 17 Constructions RD Sharma Solutions

Question 7.
The perimeter of a triangular field is 240 dm. If two of its sides are 78 dm and 50 dm, find the length of the perpendicular on the side of length 50 dm from the opposite vertex.
Solution:
Perimeter of a triangular field = 240 dm
Two sides are 78 dm and 50 dm
∴ Third side = 240 – (78 + 50)
= 240 – 128 = 112 dm
RD Sharma Book Class 9 PDF Free Download Chapter 17 Constructions
RD Sharma Class 9 Book Chapter 17 Constructions

Question 8.
A triangle has sides 35 cm, 54 cm and 61 cm long. Find its area. Also, find the smallest of its altitudes.
Solution:
Sides of a triangle are 35 cm, 54 cm, 61 cm
Constructions With Solutions PDF RD Sharma Class 9 Solutions

Question 9.
The lengths of the sides of a triangle are in the ratio 3:4:5 and its perimeter is 144 cm. Find the area of the triangle and the height corresponding to the longest side.
Solution:
Ratio in the sides of a triangle = 3:4:5
RD Sharma Class 9 Maths Book Questions Chapter 17 Constructions

Question 10.
The perimeter of an isosceles triangle is 42 cm and its base is (3/2) times each of the equal sides. Find the length of each side of the triangle, area of the triangle and the height of the triangle.
Solution:
Perimeter of an isosceles triangle = 42 cm
Base = (frac { 3 }{ 2 }) of its one of equal sides
Let each equal side = x, then 3
Base = (frac { 3 }{ 2 }) x
RD Sharma Mathematics Class 9 Solutions Chapter 17 Constructions
RD Sharma Math Solution Class 9 Chapter 17 Constructions

Question 11.
Find the area of the shaded region in figure.
RD Sharma Class 9 Questions Chapter 17 Constructions
Solution:
In ∆ABC, AC = 52 cm, BC = 48 cm
and in right ∆ADC, ∠D = 90°
AD = 12 cm, BD = 16 cm
∴ AB²=AD² + BD² (Pythagoras Theorem)
(12)² + (16)² = 144 + 256 = 400 = (20)²
∴ AB = 20 cm
Maths RD Sharma Class 9 Chapter 17 Constructions

RD Sharma Class 9 Solution Chapter 17 Constructions Ex 17.2

Question 1.
Find the area of a quadrilateral ABCD in which AB = 3cm, BC = 4cm, CD = 4cm, DA = 5cm and AC = 5cm (NCERT)
Solution:
In the quadrilateral, AC is the diagonal which divides the figure into two triangles
Now in ∆ABC, AB = 3 cm, BC = 4cm, AC = 5cm
RD Sharma Class 9 PDF Chapter 17 Constructions
Constructions Class 9 RD Sharma Solutions

Question 2.
The sides of a quadrangular field taken in order are 26 m, 27 m, 7 m and 24 m respectively. The angle contained by the last two sides is a right angle. Find its area.
Solution:
In quad. ABCD, AB = 26 m, BC = 27 m CD = 7m, DA = 24 m, ∠CDA = 90°
Join AC,
RD Sharma Class 9 Solution Chapter 17 Constructions
Class 9 RD Sharma Solutions Chapter 17 Constructions

Question 3.
The sides of a quadrilateral taken in order are 5, 12, 14 and 15 metres respectively, and the angle contained by the first two sides is a right angle. Find its area.
Solution:
In quad. ABCD,
AB = 5m, BC = 12 m, CD = 14m,
DA = 15 m and ∠ABC = 90°
Join AC,
Now in right ∆ABC,
AC² = AB² + BC² = (5)² + (12)²
= 25 + 144 = 169 = (13)²
∴ AC = 13 m
Now area of right ∆ABC
Class 9 Maths Chapter 17 Constructions RD Sharma Solutions
RD Sharma Book Class 9 PDF Free Download Chapter 17 Constructions

Question 4.
A park, in shape of a quadrilateral ABCD, has ∠C = 90°, AB = 9m, BC = 12m, CD = 5m and AD = 8m. How much area does it occupy? (NCERT)
Solution:
In quadrilateral ABCD,
AB = 9m, BC = 12m, CD = 5m and
DA = 8m, ∠C = 90°
Join BD,
Now in right ∆BCD,
BD² = BC²+ CD² = (12)² + (5)²
= 144 + 25 = 169 = (13)²
∴ BD = 13m
RD Sharma Class 9 Book Chapter 17 Constructions
Constructions With Solutions PDF RD Sharma Class 9 Solutions

Question 5.
Find the area of a rhombus whose perimeter is 80m and one of whose diagonal is 24m.
Solution:
Perimeter of rhombus ABCD = 80 m
RD Sharma Class 9 Maths Book Questions Chapter 17 Constructions

Question 6.
A rhombus sheet whose perimeter = 32 m and whose one diagonal is 10 m long, is painted on both sides at the rate of ₹5 per m². Find the cost of painting.
Solution:
Perimeter of the rhombus shaped sheet = 32 m
RD Sharma Mathematics Class 9 Solutions Chapter 17 Constructions
∴ Length of each side = (frac { 32 }{ 4 }) = 8m
and length of one diagonal AC = 10 m
In ∆ABC, sides are 8m, 8m, 10m
RD Sharma Math Solution Class 9 Chapter 17 Constructions

Question 7.
Find the area of a quadrilateral ABCD in which AD = 24 cm, ∠BAD = 90° and BCD forms an equilateral triangle whose each side is equal to 26 cm. (Take (sqrt { 3 } ) = 1.73 )
Solution:
In quadrilateral ABCD, AD = 24cm, ∠BAD = 90°
RD Sharma Class 9 Questions Chapter 17 Constructions
BCD is an equilateral triangle with side 26cm
In right ∆ABD,
BD² = AB²+ AD²
(26)² = AB² + (24)²
⇒ 676 = AB² + 576
AB² = 676 – 576 = 100 = (10)²
∴ AB = 10cm
Now area of right ∆ABD,
Maths RD Sharma Class 9 Chapter 17 Constructions

Question 8.
Find the area of a quadrilateral ABCD in which AB = 42cm, BC = 21cm, CD = 29 cm, DA = 34 cm and diagonal BD = 20 cm.
Solution:
In quadrilateral ABCD,
AB = 42 cm, BC = 21 cm, CD = 29cm DA = 34 cm, BD = 20 cm
RD Sharma Class 9 Chapter 17 Constructions
RD Sharma Class 9 Solutions Chapter 17 Constructions

Question 9.
The adjacent sides of a parallelogram ABCD measures 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of the parallelogram.
Solution:
In ||gm ABCD,
AB = 34cm, BC = 20 cm
and AC = 42 cm
RD Sharma Solutions Class 9 Chapter 17 Constructions
∵ The diagonal of a parallelogram divides into two triangles equal in area,
Now area of ∆ABC,
RD Sharma Class 9 PDF Chapter 17 Constructions

Question 10.
Find the area of the blades of the magnetic compass shown in figure. (Take (sqrt { 11 } ) = 3.32).
Constructions Class 9 RD Sharma Solutions
Solution:
ABCD is a rhombus with each side 5cm and one diagonal 1cm
Diagonal BD divides into two equal triangles Now area of ∆ABD,
RD Sharma Class 9 Solution Chapter 17 Constructions

Question 11.
A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 13 cm, 14 cm and 15 cm and the parallelogram stands on the base 14 cm, find the height of the parallelogram.
Solution:
Area of a triangle with same base and area of a 11gm with equal sides of triangle are 13, 14, 15 cm
Class 9 RD Sharma Solutions Chapter 17 Constructions
Class 9 Maths Chapter 17 Constructions RD Sharma Solutions

Question 12.
Two parallel sides of a trapezium are 60cm and 77 cm and other sides are 25 cm and 26 cm. Find the area of the trapezium.
Solution:
In trapezium ABCD, AB || DC
RD Sharma Book Class 9 PDF Free Download Chapter 17 Constructions
AB = 77cm, BC = 26 cm, CD 60cm DA = 25 cm
Through, C, draw CE || DA meeting AB at E
∴ AE = CD = 60 cm and EB = 77 – 60 = 17 cm,
CE = DA = 25 cm
Now area of ∆BCE, with sides 17 cm, 26 cm, 25 cm
RD Sharma Class 9 Book Chapter 17 Constructions
Constructions With Solutions PDF RD Sharma Class 9 Solutions

Question 13.
Find the perimeter and area of the quadrilateral ABCD in which AB = 17 cm, AD = 9cm, CD = 12cm, ∠ACB = 90° and AC = 15cm.
Solution:
In right ΔABC, ∠ACB = 90°
AB² = AC² + BC²
(17)² = (15)²+ BC² = 289 = 225 + BC²
RD Sharma Class 9 Maths Book Questions Chapter 17 Constructions
RD Sharma Mathematics Class 9 Solutions Chapter 17 Constructions

Question 14.
A hand fan is made by stitching 10 equal size triangular strips of two different types of paper as shown figure. The dimensions of equal strips are 25 cm, 25 cm and 14 cm. Find the area of each types of paper needed to make the hand fan.
Solution:
In the figure, a hand fan has 5 isosceles and triangle. With sides 25 cm, 25 cm and 14 cm each.
RD Sharma Math Solution Class 9 Chapter 17 Constructions
RD Sharma Class 9 Questions Chapter 17 Constructions

Class 9 RD Sharma Solutions Chapter 17 Constructions VSAQS

Question 1.
Find the area of a triangle whose base and altitude are 5 cm and 4 cm respectively.
Solution:
In ∆ABC,
Base BC = 5cm
Altitude AD = 4cm
Class 9 RD Sharma Solutions Chapter 17 Constructions vsaqs

Question 2.
Find the area of a triangle whose sides are 3 cm, 4 cm and 5 cm respectively.
Solution:
Sides of triangle are 3 cm, 4cm and 5cm
Class 9 Maths Chapter 17 Constructions RD Sharma Solutions
RD Sharma Book Class 9 PDF Free Download Chapter 17 Constructions

Question 3.
Find the area of an isosceles triangle having the base x cm and one side y cm.
Solution:
In isosceles ∆ABC,
AB = AC = y cm
BC = x cm
RD Sharma Class 9 Book Chapter 17 Constructions

Question 4.
Find the area of an equilateral triangle having each side 4 cm.
Solution:
Each side of equilateral triangle (a) = 4cm
Constructions With Solutions PDF RD Sharma Class 9 Solutions

Question 5.
Find the area of an equilateral triangle having each side x cm.
Solution:
RD Sharma Class 9 Maths Book Questions Chapter 17 Constructions

Question 6.
The perimeter of a triangular field is 144 m and the ratio of the sides is 3 : 4 : 5. Find the area of the field.
Solution:
Perimeter of the field = 144 m
Ratio in the sides = 3:4:5
Sum of ratios = 3 + 4 + 5 = 12
RD Sharma Mathematics Class 9 Solutions Chapter 17 Constructions

Question 7.
Find the area of an equilateral triangle having altitude h cm.
Solution:
Altitude of an equilateral triangle = h
Let side of equilateral triangle = x
RD Sharma Math Solution Class 9 Chapter 17 Constructions
RD Sharma Class 9 Questions Chapter 17 Constructions

Question 8.
Let ∆ be the area of a triangle. Find the area of a triangle whose each side is twice the side of the given triangle.
Solution:
Let a, b, c be the sides of the original triangle
Maths RD Sharma Class 9 Chapter 17 Constructions
Hence area of new triangle = 4 x area of original triangle.

Question 9.
If each side of a triangle is doubled, then find percentage increase in its area.
Solution:
Sides of original triangle be a, b, c
RD Sharma Class 9 Chapter 17 Constructions
RD Sharma Class 9 Solutions Chapter 17 Constructions

Question 10.
If each side of an equilateral triangle is tripled then what is the percentage increase in the area of the triangle?
Solution:
Let the sides of the original triangle be a, b, c and area ∆, then
RD Sharma Solutions Class 9 Chapter 17 Constructions

RD Sharma Solutions Class 9 Chapter 17 Constructions MCQS

Mark the correct alternative in each of the following:
Question 1.
The sides of a triangle are 16 cm, 30 cm, 34 cm. Its area is
(a) 225 cm²
(b) 225(sqrt { 3 } ) cm²
(c) 225(sqrt { 2 } ) cm²
(d) 240 cm²
Solution:
Sides of triangle and 16 cm, 30 cm, 34 cm
Class 9 Maths Chapter 17 Constructions RD Sharma Solutions

Question 2.
The base of an isosceles right triangle is 30 cm. Its area is
(a) 225 cm²
(b) 225(sqrt { 3 } ) cm²
(c) 225(sqrt { 2 } ) cm²
(d) 450 cm²
Solution:
Base of isosceles triangle ∆ABC = 30cm
Let each of equal sides = x
Then AB = AC = x
Now in right ∆ABC,
RD Sharma Book Class 9 PDF Free Download Chapter 17 Constructions

Question 3.
The sides of a triangle are 7cm, 9cm and 14cm. Its area is
(a) 12(sqrt { 5 } ) cm²
(b) 12(sqrt { 3 } ) cm²
(c) 24 (sqrt { 5 } ) cm²
(d) 63 cm²
Solution:
RD Sharma Class 9 Book Chapter 17 Constructions

Question 4.
The sides of a triangular field are 325 m, 300 m and 125 m. Its area is
(a) 18750 m²
(b) 37500 m²
(c) 97500 m²
(d) 48750 m²
Solution:
Sides of a triangular field are 325m, 300m, 125m
Constructions With Solutions PDF RD Sharma Class 9 Solutions

Question 5.
The sides of a triangle are 50 cm, 78 cm and 112 cm. The smallest altitude is
(a) 20 cm
(b) 30 cm
(c) 40 cm
(d) 50 cm
Solution:
The sides of a triangle are 50 cm, 78 cm, 112cm
RD Sharma Class 9 Maths Book Questions Chapter 17 Constructions

Question 6.
The sides of a triangle are 11m, 60m and 61m. Altitude to the smallest side is
(a) 11m
(b) 66 m
(c) 50 m
(d) 60 m
Solution:
Sides of a triangle are 11m, 60m and 61m
RD Sharma Mathematics Class 9 Solutions Chapter 17 Constructions

Question 7.
The sides of a triangle are 11 cm, 15 cm and 16 cm. The altitude to the largest side is
RD Sharma Math Solution Class 9 Chapter 17 Constructions
RD Sharma Class 9 Questions Chapter 17 Constructions
Solution:
Sides of a triangle are 11 cm, 15 cm, 16 cm
Maths RD Sharma Class 9 Chapter 17 Constructions

Question 8.
The base and hypotenuse of a right triangle are respectively 5cm and 13cm long. Its area is
(a) 25 cm²
(b) 28 cm²
(c) 30 cm²
(d) 40 cm²
Solution:
In a right triangle base = 5 cm
base hypotenuse = 13 cm
RD Sharma Class 9 Chapter 17 Constructions
RD Sharma Class 9 Solutions Chapter 17 Constructions

Question 9.
The length of each side of an equilateral triangle of area 4 (sqrt { 3 } ) cm², is
RD Sharma Solutions Class 9 Chapter 17 Constructions
Solution:
Area of an equilateral triangle = 4(sqrt { 3 } ) cm²
Let each side be = a
RD Sharma Class 9 PDF Chapter 17 Constructions

Question 10.
If the area of an isosceles right triangle is 8cm, what is the perimeter of the triangle.
(a) 8 + (sqrt { 2 } ) cm²
(b) 8 + 4(sqrt { 2 } ) cm²
(c) 4 + 8(sqrt { 2 } ) cm²
(b) 12(sqrt { 2 } ) cm²
Solution:
Let base = x
ABC an isosceles right triangle, which has 2 sides same
⇒ Height = x
Constructions Class 9 RD Sharma Solutions
RD Sharma Class 9 Solution Chapter 17 Constructions

Question 11.
The length of the sides of ∆ABC are consecutive integers. If ∆ABC has the same perimeter as an equilateral triangle with a side of length 9cm, what is the length of the shortest side of ∆ABC?
(a) 4
(b) 6
(c) 8
(d) 10
Solution:
Side of an equilateral triangle = 9 cm
Its perimeter = 3 x 9 = 27 cm
Now perimeter of ∆ABC = 27 cm
and let its sides be x, x + 1, x +2
Class 9 RD Sharma Solutions Chapter 17 Constructions

Question 12.
In the figure, the ratio of AD to DC is 3 to 2. If the area of ∆ABC is 40cm2, what is the area of ∆BDC?
(a) 16 cm²
(b) 24 cm²
(c) 30 cm²
(d) 36 cm²
Solution:
Ratio in AD : DC = 3:2
and area ∆ABC = 40 cm²
Class 9 Maths Chapter 17 Constructions RD Sharma Solutions

Question 13.
If the length of a median of an equilateral triangle is x cm, then its area is
RD Sharma Book Class 9 PDF Free Download Chapter 17 Constructions
Solution:
∵ The median of an equilateral triangle is the perpendicular to the base also,
∴ Let side of the triangle = a
RD Sharma Class 9 Book Chapter 17 Constructions

Question 14.
If every side of a triangle is doubled, then increase in the area of the triangle is
(a) 100(sqrt { 2 } ) %
(b) 200%
(c) 300%
(d) 400%
Solution:
Let the sides of the original triangle be a, b, c
Constructions With Solutions PDF RD Sharma Class 9 Solutions
RD Sharma Class 9 Maths Book Questions Chapter 17 Constructions

Question 15.
A square and an equilateral triangle have equal perimeters. If the diagonal of the square is 1272 cm, then area of the triangle is
RD Sharma Mathematics Class 9 Solutions Chapter 17 Constructions
Solution:
A square and an equilateral triangle have equal perimeter
RD Sharma Math Solution Class 9 Chapter 17 Constructions

All Chapter RD Sharma Solutions For Class 9 Maths

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