Question

the diagnol of a square is 10square root3 units. find rhelwngths of its sides and perimeter

Answer 1

Dear student
$$\begin{gathered} \mathrm{Given}:\mathrm{diagonal}\mathrm{of}\mathrm{square}={10}^2\sqrt{3}\mathrm{units} \\ =100\sqrt{3}\mathrm{units} \\ \mathrm{We}\mathrm{know}\mathrm{that}\mathrm{if}\mathrm{d}\mathrm{is}\mathrm{the}\mathrm{diagonal}\mathrm{and}\mathrm{a}\mathrm{is}\mathrm{the}\mathrm{side}\mathrm{of}\mathrm{square} \\ \mathrm{then}\mathrm{d}=\mathrm{a}\sqrt{2} \\ \Rightarrow 100\sqrt{3}=\mathrm{a}\sqrt{2} \\ \Rightarrow \mathrm{a}=\frac{100\sqrt{3}}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}=50\sqrt{6}units \\ \mathrm{and}\mathrm{perimeter}=4\times \mathrm{side} \\ =4\times 50\sqrt{6} \\ =200\sqrt{6}\mathrm{units}. \end{gathered}$$
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