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:

$$\begin{gathered} a=5\text{ m } \\ q=1+{\displaystyle \frac{10.25}{100}}={\displaystyle \frac{441}{400}}=1.1025 \\ S=a^2=5^2=25{\text{m}}^2 \\ {S}_1=q\cdot S=1.1025\cdot 25={\displaystyle \frac{441}{16}}=27.5625{\text{m}}^2 \\ {a}_1=\sqrt{S_1}=\sqrt{27.5625}={\displaystyle \frac{21}{4}}=5.25 \\ {p}_1=100\cdot {\displaystyle \frac{a_1-a}{a}}=100\cdot {\displaystyle \frac{5.25-5}{5}}=5\mathrm{\%} \end{gathered}$$

$$\begin{gathered} o=4\cdot a=4\cdot 5=20\text{ m } \\ {o}_1=4\cdot a_1=4\cdot 5.25=21\text{ m } \\ {p}_2=100\cdot {\displaystyle \frac{o_1-o}{o}}=100\cdot {\displaystyle \frac{21-20}{20}}=5\mathrm{\%} \end{gathered}$$

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