Question

If the side of a square is increased by 50%. The percent increase in area is :

• A. $50$
• B. $100$
• C. $125$
• D. $150$

Answer 1

Answer: (C)

$125$

Let side of square $=x$

Area $=x^2$

After 50% increase in side

side length $=x+50$% of x

$=\frac{3}{2}x$

Area $={\left(\frac{3x}{2}\right)}^2=\frac{9}{4}{x}^2$

percentage increase in are $=\frac{Ainitial-Ainitial}{Ainitial}\times 100$

$=\frac{\frac{9}{4}{x}^2-x^2}{x^2}\times 100$

$=\frac{5}{4}\frac{x^2}{x^2}\times 100=125$%