Question

The perimeter of a parallelogram is 150cm. If one of the sides is longer than the other by 15cm , find the length of each of its sides.

Answer 1

Answer:

Let a parallelogram ABCD ,such that its shorter sides are AD & BC. and the longer sides are AB & DC.

Now, let the length of Shorter sides be

x cm,

then according to the question the length of longer sides will be

(x+15) cm.

also , we know that the lengths of opposite sides of a parallelogram are equal, thus we have,

AD = BC = x cm and

AB = DC = (x+15) cm.

Note: The perimeter of a polygon is equal to the sum of lengths of all its boundaries (sides).

For a parallelogram,

Perimeter = 2(sum of adjacent sides)

now,

It is given that,

The perimeter of the parallelogram is equal to 150 cm.

Thus,

=> 2(AD+AB) = 150

=> 2(x+x+15) = 150

=> 2(2x+15) = 150

=> 2x + 15 = 150/2

=> 2x + 15 = 75

=> 2x = 75 - 15

=> 2x = 60

=> x = 60/2

=> x = 30

Thus,

The lengths of each sides of the parallelogram are as:

AD = BC = 30 cm

AB = DC = (30+15)cm = 45 cm

ie,

AB = 45 cm

BC = 30 cm

CD = 45 cm

DA = 30 cm.