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 m q=1+10.25100=441400=1.1025  S=a2=52=25 m2 S1=q⋅ S=1.1025⋅ 25=44116=27.5625 m2  a1=S1=27.5625=214=5.25  p1=100⋅ a1−aa=100⋅ 5.25−55=5%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⋅ a=4⋅ 5=20 m o1=4⋅ a1=4⋅ 5.25=21 m p2=100⋅ o1−oo=100⋅ 21−2020=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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