Question

If the area of a square reduces by 51%, the percentage reduction in its perimeter will be:

• A. 49%
• B. 70%
• C. 30%
• D. 51%

Answer 1

Answer: (C)

Given:
Area of square reduced by 51%
Let the new area be $Area=A-0.51A$ =$0.49A$
$⟹side=\sqrt{0.49a^2}=0.7a$
$\therefore thenewperimeter=4\cdot newside$
$⟹4\cdot 0.7a=2.8a$
$\therefore Thedifferenceinperimeter=\frac{4a-2.8a}{4a}$
$⟹NewPerimeter=0.3$
The perimeter is reduced by 30%