Question

The square of a diagonal is 128 cm. Find the side of the square.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{each}\mathrm{side}\mathrm{of}\mathrm{square}=\mathrm{s}\mathrm{cm} \\ \mathrm{Now},\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{diagonal},\mathrm{d}=\sqrt{2}\mathrm{s} \\ \mathrm{Now},{\mathrm{d}}^2=128{\mathrm{cm}}^2 \\ \Rightarrow {\left(\sqrt{2}\mathrm{s}\right)}^2=128 \\ \Rightarrow 2{\mathrm{s}}^2=128 \\ \Rightarrow {\mathrm{s}}^2=64 \\ \Rightarrow \mathrm{s}=8\mathrm{cm} \\ \mathrm{So},\mathrm{length}\mathrm{of}\mathrm{each}\mathrm{side}\mathrm{of}\mathrm{square}=8\mathrm{cm} \end{gathered}$$