Given: Length of rectangle increases by 20%
Breadth of rectangle reduces by 15%
Formula used: Area of a rectangle = Length × Breadth
and Percentage =
(Favourablevalue) × 100
Calculation: Let the original length and breadth of the rectangle be x cmand y cm respectively.
Then, Area of the rectangle = x × y = xy
cm2 New length = [1 + (
)] × x
⇒ (
) × x
⇒ 1.2x cm
and new breadth = [1 – (
)] × y
⇒ (
) × y
⇒ 0.85 y cm
So, New area of the rectangle = 1.2x × 0.85y
⇒ 1.02xy
cm2 Difference in area = 1.02xy
cm2 – xy
cm2 = 0.02xy
cm2 ⇒ Net percentage change = [
] × 100
⇒ 0.02 × 100
⇒ 2%
∴ The area of the rectangle increases by 2%.