Question

Area of a square is increased by $44\%$ without changing its shape. Find the percentage increase on each side.

• A. $20\%$
• B. $25\%$
• C. $10\%$
• D. $50\%$

Answer 1

The correct option is A $20\%$

Let the original square be of side length $1$ unit.
Its area will be $A=1\times 1=1$ sq unit.

Area is increased by $44\%=\frac{44}{100}\times 1=0.44$ sq units

Let $“x”$ be the increase in each side of the square.

Hence, the new side is $1+x.$
Final area of the square $=1+0.44=1.44$ sq units
$(1+x{)}^2=1.44$

Taking square root on both the sides:
$(1+x)=1.2$
$x=1.2-1$
$x=0.2$
Percentage increase in each side $=\frac{\text{Increase in side length}}{\text{Original side}}\times 100$
$=\frac{0.2}{1}\times 100$
$=20\%$

Each side of the square has increased by $20\%$