Question

​Find the length of a side of a square if the length of it's diagonal is 10 cm.

Answer 1

Dear student

$$\begin{gathered} \mathrm{We}\mathrm{know}\mathrm{that} \\ \mathrm{diagonal},\mathrm{d}=\mathrm{a}\sqrt{2},\mathrm{where}\mathrm{a}\mathrm{is}\mathrm{the}\mathrm{side}\mathrm{of}\mathrm{the}\mathrm{square} \\ \Rightarrow 10=\mathrm{a}\sqrt{2}\left(\mathrm{given},\mathrm{d}=10\mathrm{cm}\right) \\ \Rightarrow 100=2{\mathrm{a}}^2 \\ \Rightarrow 50={\mathrm{a}}^2 \\ \Rightarrow \mathrm{a}=5\sqrt{2}\mathrm{cm}\left[\mathrm{length}\mathrm{cannot}\mathrm{be}\mathrm{negative}\right] \end{gathered}$$
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