Question

The perimeter of a parallelogram is 150 cm, and one of its side is greater than the other by 25cm. find the lengths of all the sides of that parallelogram.

Answer 1

Let ABCD be a parallelogram in which side AB is greater than side BC by 25 cm.
Then,
AB = x cm and BC = (x + 25) cm


We know that opposite sides of a parallelogram are congruent.
Thus, we have:
AD = BC = (x + 25) cm and CD = AB= x cm
Now,
Perimeter of the parallelogram = AB + BC + CD + DA
$\Rightarrow$ x + x + 25 + x + x + 25 = 150
$\Rightarrow$ 4x + 50 = 150
$\Rightarrow$ 4x = 150 – 50
$\Rightarrow$ 4x = 100
$\Rightarrow$ x = $\frac{100}{4}$
$\Rightarrow$ x = 25
Thus, we have
AB = CD
= 25 cm
BC = AD
= (25 + 25) cm
= 50 cm
Therefore, the sides of the parallelogram are 25 cm, 50 cm, 25 cm and 50 cm.