Question

The perimeter of a rectangle is 240 cm. If its length is increased by 10% and its breadth is decreased by 20%, we get the same perimeter. Find the length and breadth of the rectangle.

Answer 1

Given, perimeter of rectangle = 240 cm

⇒ 2 × (Length + Breadth) = 240 cm

⇒ Length + Breadth = 120 cm

Let the length of rectangle be x cm

Then, the breadth of rectangle = (120 – x) cm

∴ New length of rectangle = x + 10% of x

= `x + 10/100 xx x`

= `110/100 x  cm`

And new breadth of rectangle = (120 – x) – 20% of (120 – x) cm

= `(120 - x) - 20/100 xx (120 - x)`

= `(120 - x)(1 - 20/100)`

= `80/100 (120 - x)  cm` 

It is given that, perimeter of new rectangle is 240 cm.

According to the question,

2 × (New length + New breadth) = 240

⇒ `2 xx [(110x)/100 + 80/100 (120 - x)] = 240`

⇒ `(110x + 9600 - 80x)/100 = 240/2`

⇒ `30x + 9600 = 240/2 xx 100`

⇒ 30x + 9600 = 12000

⇒ 30x = 12000 – 9600

⇒ 30x = 2400

⇒ x = `2400/30` = 80

Hence, length of rectangle = 80 cm

And breadth of rectangle = 120 – 80 = 40 cm.