Percentage and rectangle

About what percentage increases perimeter and area of a rectangle if both the sides 12 cm and 10 cm long we increase by 20%?

Correct answer:

p₁ =  20 %
p₂ =  44 %

Step-by-step explanation:

$$\begin{gathered} a=12 \\ b=10 \\ S=a\cdot b=12\cdot 10=120 \\ o=2\cdot (a+b)=2\cdot (12+10)=44 \\ {a}_1=a\cdot 1.20=12\cdot 1.20={\displaystyle \frac{72}{5}}=14.4 \\ {b}_1=b\cdot 1.20=10\cdot 1.20=12 \\ {S}_1=a_1\cdot b_1=14.4\cdot 12={\displaystyle \frac{864}{5}}=172.8 \\ {o}_1=2\cdot (a_1+b_1)=2\cdot (14.4+12)={\displaystyle \frac{264}{5}}=52.8 \\ {p}_1=p_1=100\cdot (o_1-o)\mathrm{/}o=100\cdot (52.8-44)\mathrm{/}44=20\mathrm{\%} \end{gathered}$$

$p_2=p_2=100\cdot (S_1-S)\mathrm{/}S=100\cdot (172.8-120)\mathrm{/}120=44\mathrm{\%}$

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