Rectangular land

Due to the new road, the longer dimension of the rectangular plot had to be shortened by 4 percent, and the shorter dimension shrunk by 10 percent. Thus, the area of the land has decreased by how much percent?

Correct answer:

p =  13.6 %

Step-by-step explanation:

$$\begin{gathered} q_1=100\%-4\%=1-\frac{4}{100}=0.96 \\ {q}_2=100\%-10\%=1-\frac{10}{100}=0.9 \\ S=a\cdot b \\ r=q_1\cdot q_2=0.96\cdot 0.9=\frac{108}{125}=0.864 \\ {S}_1=r\cdot S \\ p=100\cdot (1-r)=100\cdot (1-0.864)=13.6\% \end{gathered}$$

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