The sides 6

The sides of the rectangle are 12 cm and 15 cm. How many percent will the area of the rectangle increase if we increase each side by 10%?

Final Answer:

p =  21 %

Step-by-step explanation:

$$\begin{gathered} a=12\text{cm} \\ b=15\text{cm} \\ q=100\%+10\%=1+\frac{10}{100}=1.1 \\ x=q\cdot a=\frac{11}{10}\cdot 12=\frac{11\cdot 12}{10}=\frac{132}{10}=\frac{66}{5}=13.2\text{cm} \\ y=q\cdot b=\frac{11}{10}\cdot 15=\frac{11\cdot 15}{10}=\frac{165}{10}=\frac{33}{2}=16.5\text{cm} \\ {S}_1=a\cdot b=12\cdot 15=180{\text{cm}}^2 \\ {S}_2=x\cdot y=\frac{66}{5}\cdot \frac{33}{2}=\frac{66\cdot 33}{5\cdot 2}=\frac{2178}{10}=\frac{1089}{5}=217.8{\text{cm}}^2 \\ p=100\cdot \frac{S_2-S_1}{S_1}=100\cdot \frac{\frac{1089}{5}-180}{180}=21\% \end{gathered}$$

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