Question

The width of a square increases by $30\%$. By what percent does its area increase?

• A. $30\%$
• B. $69\%$
• C. $90\%$
• D. $105\%$
• E. $900\%$

Answer 1

Answer: (B)

$69\%$

Let the width of the square be $=w$
The new width $=w+30$ $\%$ of $w=w+\frac{30}{100}\times w=1.3w$
Original area of the square $=w^2$
New area of the square $=(1.3w{)}^2=1.69w^2$
Percent increase in the area $=\frac{1.69w^2-w^2}{w^2}\times 100=0.69\times 100=69$ $\%$