# 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:

$a = 5 \ m \ \\ q = 1 + \dfrac{ 10.25 }{ 100 } = \dfrac{ 441 }{ 400 } = 1.1025 \ \\ \ \\ S = a^2 = 5^2 = 25 \ m^2 \ \\ S_{ 1 } = q \cdot \ S = 1.1025 \cdot \ 25 = \dfrac{ 441 }{ 16 } = 27.5625 \ m^2 \ \\ \ \\ a_{ 1 } = \sqrt{ S_{ 1 } } = \sqrt{ 27.5625 } = \dfrac{ 21 }{ 4 } = 5.25 \ \\ \ \\ p_{ 1 } = 100 \cdot \ \dfrac{ a_{ 1 }-a }{ a } = 100 \cdot \ \dfrac{ 5.25-5 }{ 5 } = 5 = 5 \%$
$o = 4 \cdot \ a = 4 \cdot \ 5 = 20 \ m \ \\ o_{ 1 } = 4 \cdot \ a_{ 1 } = 4 \cdot \ 5.25 = 21 \ m \ \\ p_{ 2 } = 100 \cdot \ \dfrac{ o_{ 1 }-o }{ o } = 100 \cdot \ \dfrac{ 21-20 }{ 20 } = 5 = 5 \%$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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