If the side of a square is increased by 25% , then its area is increas

Question

If the side of a square is increased by

25 %

, then its area is increased by how many percent?

Options:

A . 50%

B . 58%

C . 56.25%

D . >60%

Answer: Option C
:
C
Let the side be 10 cm. Then the area will be

100 c m^{2}

New side

= 125 % o f 10 = 12.5 c m;

A r e a = (12.5)^{2} = 156.25

Percentage increase in area

= 56.25 % .

Alternatively:If x is the percentage increase in the side of a square, then increase in area is given by

x + x + \frac{x \times x}{100} = 2 x + \frac{x^{2}}{100} = 25 + 25 + \frac{25 \times 25}{100} = 56.25 %

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