## Chapter 20 - Constructions of Quadrilaterals Exercise Ex. 20.1

Question 1
Solution 1

Question 2
Solution 2

Question 3
Solution 3

Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7

Question 8
Solution 8
Question 9
Solution 9

Question 10
Solution 10
Question 11
Solution 11

Question 12
Solution 12

Question 13
Solution 13
Question 14
Construct a rectangle ABCD, when
AD = 3.2cm and diagonal BD = 5.5cm. Measure CD.
Solution 14
Steps of construction:
1. Draw AD = 3.2 cm
2. Draw ∠XAD = 90°.
3. With D as centre and radius BD = 5.5 cm, draw an arc to cut AX at point B.
4. Join BD.
5. With B as centre and radius 3.2 cm draw an arc and with D as centre and radius = AB, draw another arc to cut the previous arc at C.
6. Join BC and CD.
Thus, ABCD is the required rectangle.
CD = 4.5 cm

Question 15
Construct a rectangle ABCD, when
AB = 5cm and BC = 6.2cm.
Solution 15
Steps of construction:
1. Draw BC = 6.2 cm
2. Through B, draw BP such that ∠B = 90°
3. From BP, cut BA = 5 cm
4. With A and C as centres and radii 6.2 cm and 5 cm respectively, draw arcs cutting each other at D.
5. Join AD and CD.
Thus, ABCD is the required triangle.

Question 16
Solution 16

Question 17
Solution 17

Question 18
Solution 18
Question 19
Construct a rectangle PQRS, when its
Area = 21 cm2 and length = 4.2cm
Solution 19
Since area of rectangle = 21 cm2
And, length = 4.2 cm
Breadth = Area ÷ Length = 21 ÷ 4.2 = 5 cm
Steps of construction:
1. Draw BC = 5 cm
2. Through B, draw BP such that ∠B = 90°
3. From BP, cut BA = 4.2 cm
4. With A and C as centres and radii 5 cm and 4.2 cm respectively, draw arcs cutting each other at D.
5. Join AD and CD.
Thus, ABCD is the required triangle.

Question 20
Construct a rectangle PQRS, when its
Area = 33.8cm2 and breadth = 6.5cm
Solution 20
Since area of rectangle = 33.8 cm2
And, breadth = 6.5 cm
Length = Area ÷ Breadth = 33.8 ÷ 6.5 = 5.2 cm
Steps of construction:
1. Draw BC = 6.5 cm
2. Through B, draw BP such that ∠B = 90°
3. From BP, cut BA = 5.2 cm
4. With A and C as centres and radii 6.5 cm and 5.2 cm respectively, draw arcs cutting each other at D.
5. Join AD and CD.
Thus, ABCD is the required triangle.
Question 21
Solution 21
Question 22
Solution 22