Percent change

The length of a rectangle is increased by 25%, and the width is decreased by 10%. By what percent is the area of the rectangle larger than the area of the original rectangle?

Correct answer:

p =  12.5 %

Step-by-step explanation:

$$\begin{gathered} q_1=1+25/100=\frac{5}{4}=1.25 \\ {q}_2=1-10/100=\frac{9}{10}=0.9 \\ {S}_1=ab \\ {S}_2=(a\cdot q_1)\cdot (b\cdot q_2) \\ p=100\cdot \frac{S_2-S_1}{S_1} \\ p=100\cdot \frac{(a\cdot q_1)\cdot (b\cdot q_2)-ab}{ab} \\ p=100\cdot \frac{q_1\cdot q_2-1}{1}=100\cdot \frac{\frac{5}{4}\cdot \frac{9}{10}-1}{1}=\frac{25}{2}\%=12.5\% \end{gathered}$$

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