The length of a rectangle is increased by 25%. By what percentage should the width be decreased so that the area of the rectangle remains unchanged?

Question: The length of a rectangle is increased by 25%. By what percentage should the width be decreased so that the area of the rectangle remains unchanged?

Solution:
Let,
original length = L₁, width = W₁, area = L₁ × W₁
As the length of a rectangle is increased by 25% of original length,
∴ New length, L₂= L₁+ 25% of L₁ = L₁ + 0.25L₁ = 1.25L₁
Let,
New Width = W₂
So new area = L₂ × W₂

As Area unchanged,
We can write,
L₂ × W₂ = L₁ × W₁
⇒ 1.25L₁ × W₂ = L₁ × W₁
⇒ 1.25W₂ = W₁
⇒ W₂ = W₁/1.25
∴ W₂ = 0.8W₁
Decrease in width = W₁ - W₂
=W₁ - 0.8W₁ = 0.2W₁,
So the percentage of width decrease = (0.2W₁/W₁) × 100%
= 20%