Question

a parallelogram is such that its length is 5cm less than twice its breadth. if the perimeter of the parallelogram is 44cm , find the length of its sides.​

Answer 1

The sides of the parallelogram :-

• The length of the parallelogram = 13 cm.
• The breadth of the parallelogram = 9 cm.

Given :

• The length of the parallelogram is 5 cm less than twice its breadth.
• The perimeter of the parallelogram = 44 cm.

To Find :

• The length of the parallelogram.
• The breadth of the parallelogram.

Solution :

Let,

The length of the parallelogram be x.

The breadth of the parallelogram be y.

According to the condition,

The length of the parallelogram is 5 cm less than twice its breadth.

$\bf \implies x = 2y - 5 \: \: .........(1)$

Given,

The perimeter of the parallelogram = 2 (l + b)

Where,

• l = length.
• b = breadth.

First, we have to find the breadth of the parallelogram.

We can substitute the equation (1) in the formula of the perimeter of the parallelogram.

$\bf \implies 2 \bigg(2y - 5 + y \bigg) = 44 \: cm \\ \\ \\ \bf \implies 2y - 5 + y = \dfrac{44}{2} \: cm \\ \\ \\ \bf \implies 2y + y - 5 = 22 \: cm \\ \\ \\ \bf \implies 3y - 5 = 22 \: cm \\ \\ \\ \bf \implies 3y = 22 + 5 \: cm \\ \\ \\ \bf \implies 3y = 27 \: cm \\ \\ \\ \bf \implies y = \dfrac{27}{3} \: cm \\ \\ \\ \bf \implies y = 9 \: cm \\ \\ \\ \: \: \therefore \bf \: \: Breadth = 9 \: cm$

Hence, the breadth of the parallelogram is 9 cm.

Now, we have to find the length of the parallelogram.

We can substitute the breadth of the parallelogram in the equation (1),

$\bf \implies x = 2y - 5 \\ \\ \\ \bf \implies x = 2(9 \: cm) - 5 \\ \\ \\ \bf \implies x = 18 \: cm - 5 \\ \\ \\ \bf \implies x = 13 \: cm \\ \\ \\ \: \: \therefore \: \: \bf Length = 13 \: cm$

Hence, the length of the parallelogram is 13 cm.

Hence,

The length and the breast of the parallelogram is 13 cm and 9 cm.

_______________________________

Verification :

Given,

The perimeter of the parallelogram = 44 cm

$\bf \implies 2(l + b) = 44 \: cm$

Where,

• l = length = 13 cm.
• b = breadth = 9 cm.

$\bf \implies 2(13 \: cm + 9 \: cm) = 44 \: cm \\ \\ \\ \bf \implies 2(22 \: cm) = 44 \: cm \\ \\ \\ \bf \implies 44 \: cm = 44 \: cm$

Hence Verified !