Question

The length of a rectangle is decreased by 50%. What percentage the width have to increased so as to maintain the same area :

• A. 100
• B. 50
• C. 75
• D. 120

Answer 1

Answer:

A. 100

length = l breadth = b

area = $l \times b$

given length is decreased by 50%

so new length = $\frac{l}{2}$

new area =$\frac{l}{2}\times \text{b}$

given new area = area

$\frac{l}{2}\times \text{b} = l \times b$

divide both side by $\frac{l}{2}$

new breadth = $\frac{l \times b}{\frac{l}{2}}$

new breadth =$2\times b$

percentage increase = $\frac{2b-b}{b}\times 100$

= 100%