# 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?

Correct result:

p1 =  5 %
p2 =  5 %

#### Solution:

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

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