Question

The adjacent sides of a parallelogram are 32 cm and 24 cm. If the distance between the longer sides is 17.4 cm, find the distance between the shorter sides.

Answer 1

Given :
Two adjacent sides of the parallelogram are AB = 32 cm and BC = 24 cm
and the distance between the longer side, DE = 17.4 cm.

To find the distance between the shorter side.

Let the distance between the shorter side, DF be 'y' cm.

Area of the parallelogram = Base × Height

Area of the parallelogram, considering AB as the base = AB × DE
= 32 × 17.4
Area = 556.8 cm²

Now considering BC as the base, the area of the parallelogram = BC × DF
= 24 × y
Area = 24y

Since the area of the parallelogram will be the same, if we consider Ab as the base or BC as the base.
So, AB × DE = BC × DF
⇒ 556.8 = 24y
⇒ x = $\frac{556.8}{24}$
⇒ x = 23.2 cm
So, the distance between the shorter side is 23.2 cm.