Garden diagonal length

The garden has a square shape, and its area is 8,100 m². It will be divided by a sidewalk connecting the two opposite garden peaks. How long will this trail be?

Final Answer:

x =  127.2792 m

Step-by-step explanation:

$$\begin{gathered} S=8100{\text{m}}^2 \\ S=a^2 \\ a=\sqrt{S}=\sqrt{8100}=90\text{m} \\ {a}^2+a^2=x^2 \\ 2a^2=x^2 \\ x=\sqrt{2}\cdot a=\sqrt{2}\cdot 90=90\sqrt{2}=127.2792\text{m} \end{gathered}$$

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