# Square side

If we enlarge the square side a = 5m, its area will increase by 10,25%. How many percent will the side of the square increase? How many percent will it increase the circumference of the square?

Result

p1 =  5 %
p2 =  5 %

#### Solution:

$a = 5 \ m \ \\ q = 1 + \dfrac{ 10.25 }{ 100 } = \dfrac{ 441 }{ 400 } = 1.1025 \ \\ \ \\ S = a^2 = 5^2 = 25 \ m^2 \ \\ S_{ 1 } = q \cdot \ S = 1.1025 \cdot \ 25 = \dfrac{ 441 }{ 16 } = 27.5625 \ m^2 \ \\ \ \\ a_{ 1 } = \sqrt{ S_{ 1 } } = \sqrt{ 27.5625 } = \dfrac{ 21 }{ 4 } = 5.25 \ \\ \ \\ p_{ 1 } = 100 \cdot \ \dfrac{ a_{ 1 }-a }{ a } = 100 \cdot \ \dfrac{ 5.25-5 }{ 5 } = 5 = 5 \%$
$o = 4 \cdot \ a = 4 \cdot \ 5 = 20 \ m \ \\ o_{ 1 } = 4 \cdot \ a_{ 1 } = 4 \cdot \ 5.25 = 21 \ m \ \\ p_{ 2 } = 100 \cdot \ \dfrac{ o_{ 1 }-o }{ o } = 100 \cdot \ \dfrac{ 21-20 }{ 20 } = 5 = 5 \%$

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