Question

(a) Construct a parallelogram ABCD such that BC=4.5 cm, BD=4 cm and

AC= 5.6 cm.


(b) Two adjacent sides of a parallelogram are 24cm and 18 cm. If the distance

between longer sides is 12cm, find the distance between shorter sides.​

Answer 1

(a) Steps of Construction:

(i) Draw a triangle BOC with BC=4.5cm

Here,

BO=1/2×4=2cm

OC=1/2AC

=1/2×5.6

=2.8cm

We know that the diagonals of parallelogram bisect each other.

(ii) Produce OC to point A such that OC=OA.

(iii) Produce BO to point D such that OD=OB.

(iv) Now join AD.

Therefore, ABCD is the required parallelogram

(b) The length of side 24cm

Its corresponding height is 12cm

The area of parallelogram is 24×12=288cm²

The length of another side is 18cm

The area of parallelogram is 288cm²

Its corresponding height is 288/18=16cm