Square side

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

Correct answer:

p₁ =  5 %
p₂ =  5 %

Step-by-step explanation:

$$\begin{gathered} a=5\text{m} \\ q=1+\frac{10.25}{100}=\frac{441}{400}=1.1025 \\ S=a^2=5^2=25{\text{m}}^2 \\ {S}_1=q\cdot S=\frac{441}{400}\cdot 25=\frac{441\cdot 25}{400}=\frac{11025}{400}=\frac{441}{16}=27.5625{\text{m}}^2 \\ {a}_1=\sqrt{S_1}=\sqrt{27.5625}=\frac{21}{4}=5.25 \\ {p}_1=100\cdot \frac{a_1-a}{a}=100\cdot \frac{\frac{21}{4}-5}{5}=5\% \end{gathered}$$

$$\begin{gathered} o=4\cdot a=4\cdot 5=20\text{m} \\ {o}_1=4\cdot a_1=4\cdot \frac{21}{4}=\frac{4\cdot 21}{4}=\frac{84}{4}=21\text{m} \\ {p}_2=100\cdot \frac{o_1-o}{o}=100\cdot \frac{21-20}{20}=5\% \end{gathered}$$

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