Given: Length of rectangle increases by 20% Breadth of rectangle reduces by 15% Formula used: Area of a rectangle = Length × Breadth and Percentage = (Favourable‌
Value
Base
‌value) × 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 + (
20
100
)] × x ⇒ (
120
100
) × x ⇒ 1.2x cm and new breadth = [1 – (
15
100
)] × y ⇒ (
85
100
) × 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 = [
(0.02‌xy)
xy
] × 100 ⇒ 0.02 × 100 ⇒ 2% ∴ The area of the rectangle increases by 2%.