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Perimeter of a parallelogram is 150 cm. One of its sides is greater than the other side by 25 cm. Find the lengths of all sides.

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Best answer

i. Let ABCD be the parallelogram and the length of AD be x cm. 

One side is greater than the other by 25 cm. 

∴ AB = x + 25 cm 

AD = BC = x cm 

AB = DC = (x + 25) cm [Opposite angles of a parallelogram] 

ii. Perimeter of ABCD = 150 cm [Given] 

∴ AB + BC + DC + AD = 150 

∴ (x + 25) + x + (x + 25) + x – 150

∴ 4x + 50 = 150 

∴ 4x = 150 – 50 

∴ 4x = 100

∴ x = 100/4 

∴ x = 25

iii. AD = BC = x = 25 cm 

AB = DC = x + 25 = 25 + 25 = 50 cm 

∴ The lengths of the sides of the parallelogram are 25 cm, 50 cm, 25 cm and 50 cm.

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