Question

Ex. 7. The length of a rectangle is increased by 30%. By what percent would the breadth have to be decreased to
maintain the same area?
​

Answer 1

Given info : The length of a rectangle is increased by 30% .

To find : the percentage decrease in the breadth to maintain the same area.

solution : let length and breadth of a rectangle is l and b respectively.

so, area of rectangle , A = l × b

now length of the rectangle is increased by 30%

so, l' = l + 30% of l = 1.3 l

as area of rectangle remains same.

so, l × b = 1.3l × b'

⇒b' = b/1.3

so, percentage decrease in breadth = (b - b')/b × 100

= (b - b/1.3)/b × 100

= 0.3/1.3 × 100

= 30/1.3

= 23.076 %

therefore the percentage decrease in the breadth of the rectangle is 23.076 % to maintain the same area.