A baseball diamond is a square with an area of 8100 square feet. The length of the diagonal of any square is equal to $$\sqrt2$$ times its side length. Find the distance from home plate to second base (the length of the diagonal) to the nearest hundredth of a foot.

$$a-the\ sides\ of\ the\ square\\\\A_{\fbox{}}=a^2;\ A_{\fbox{}}=8100ft^2\\\\a^2=8100ft^2\\\\a=\sqrt{8100ft^2}\\\\a=90ft\\-\\The\ diagonal\ of\ the\ square: d=a\sqrt2\\-\\The\ distance\ from\ home\ plate\ to\ second\ base:\\\\d=90\sqrt2\ ft\approx(90\times1.414)ft=\boxed{127.26ft}$$

$$A_{square}=(the\ side\ of\ the\ square)^2\\\\A_{square}=8100\ ft^2\ \ \ \Leftrightarrow\ \ \ A_{square}=(90\ ft)^2\\\\(the\ side\ of\ the\ square)^2=(90\ ft)^2\ \ and\ \ \ the\ side\ of\ the\ square>0\\\\the\ side\ of\ the\ square=91\ ft\\\\the\ length\ of\ the\ diagonal= \sqrt{2} \cdot the\ side\ length\ (of\ the\ square)\\\\the\ length\ of\ the\ diagonal= \sqrt{2} \cdot 90\ ft\\\\ \sqrt{2} =1.4142135623.\approx1.4142\\\\$$

$$\Rightarrow\ \ \ the\ length\ of\ the\ diagonal\approx1.4142\cdot90\ ft=127.278\ ft$$

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