Question

The ratio of two sides of a parallelogram is 3 : 5 and its perimeter is 48 cm. Find the sides of the parallelogram.

Answer 1

Let ABCD be a parallelogram in which the ratio of two sides AB and BC is 3 : 5
Thus, we have:
AB = 3x cm and BC = 5x cm

We know that opposite sides of a parallelogram are congruent (equal).
Thus, we have:
AD = BC = 5x and CD = AB = 3x
Now,
Perimeter of the parallelogram= AB + BC + CD + AD
$\Rightarrow 3x+5x+3x+5x=48$ [$\because$ Perimeter of parallelogram $=48cm$ (given)]
$\Rightarrow 16x=48$
$\Rightarrow x=\frac{48}{16}$
$\Rightarrow x=3cm$
Thus, we get:
$AB=CD=3x=3\times 3=9cm$
$BC=AD=5x=5\times 3=15cm$
Therefore, the sides of the parallelogram are 9 cm, 15 cm, 9 cm, and 15 cm.