Garden path decrease

A new path is to lead through Mr. Milo's garden – diagonally. By what percentage of the area of the park will it decrease? The length is 23.8 m, the width is 16.7 m, and the road width is 6 m.

Final Answer:

p =  43.8905 %

Step-by-step explanation:

$$\begin{gathered} a=23.8\text{m} \\ b=16.7\text{m} \\ c=6\text{m} \\ {S}_1=a\cdot b=23.8\cdot 16.7=\frac{19873}{50}=397.46{\text{m}}^2 \\ d=\sqrt{a^2+b^2}=\sqrt{23.8^2+16.7^2}\doteq 29.0746\text{m} \\ {S}_2=d\cdot c=29.0746\cdot 6\doteq 174.4474{\text{m}}^2 \\ p=100\cdot \frac{S_2}{S_1}=100\cdot \frac{174.4474}{397.46}=43.8905\% \end{gathered}$$

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