# Square

If we increase side of the square, increase its area of 63%.
What is the percentage we increase side of the square?

Result

p =  27.7 %

#### Solution:

$S=a^2 \ \\ S(1+\dfrac{ 63}{100}) = (a(1+\dfrac{p}{100}))^2 \ \\ S \cdot 1.63 = (a(1+\dfrac{p}{100}))^2 \ \\ a^2\cdot 1.63 = (a(1+\dfrac{p}{100}))^2 \ \\ 1.63 = (1+\dfrac{p}{100})^2 \ \\ \sqrt{ 1.63} = 1+\dfrac{p}{100} \ \\ \sqrt{ 1.63 } -1 = \dfrac{p}{100} \ \\ 100(\sqrt{ 1.63 } -1) = p \ \\ 27.7 \% = p$

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