Square side increase

We increased the side of the square by 12% from the original 15cm.
For a, what was the perimeter and area of the new square?
By what percent did the perimeter and area increase?

Final Answer:

o₂ =  67.2 cm
S₂ =  282.24 cm²
p₁ =  12 %
p₂ =  25.44 %

Step-by-step explanation:

$$\begin{gathered} a=15\text{cm} \\ r=100\%+12\%=1+\frac{12}{100}=1.12 \\ b=a\cdot r=15\cdot 1.12=\frac{84}{5}=16.8\text{cm} \\ {o}_1=4\cdot a=4\cdot 15=60 \\ {o}_2=4\cdot b=4\cdot 16.8=67.2\text{cm} \end{gathered}$$

$$\begin{gathered} S_1=a^2=15^2=225{\text{cm}}^2 \\ {S}_2=b^2=16.8^2=282.24{\text{cm}}^2 \end{gathered}$$

$p_1=100\cdot \frac{o_2-o_1}{o_1}=100\cdot \frac{67.2-60}{60}=12\%$

$p_2=100\cdot \frac{S_2-S_1}{S_1}=100\cdot \frac{282.24-225}{225}=25.44\%$

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