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How much will the area increase, if each side of a square is increased by 25%?

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55%

50%

56.25%

55.25%

answer is B.

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Detailed Solution

Let each side of the square be x.
The sides of the square are getting increased by 25%, so the new side will be

x + 25 % x

.
New side=

x + 25100 x

= 100 x + 25 x 100

= 125 x 100

= 5 x 4

We have to find the increase in area for which we will subtract the area of a square with the new side from the area of the square with the original side.
Increase in area

= 5 x 4 2 − x 2

= 25 x 2 16 − x 2

= 25 x 2 − 16 x 2 16

= 9 x 2 16

56.25 x 2

So, the area of the square increases by 56.25%.
Hence, option 2 is correct.

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