Question

The length of diagonal of a square is 13 cm. then find the length of each side.

Answer 1

Let $\square$ABCD be a square in which AC = BD = 13 cm.

In ΔABC, $\angle$ABC = 90°. (An angle of a square)
By Pythagoras's theorem, we have:
AC² = AB² + BC²
$\Rightarrow$(13)² = AB² + AB² (All sides of a square are equal.)
$\Rightarrow$(13)² = 2AB²
$\Rightarrow$(13)² = $(\sqrt{2}\mathrm{AB}{)}^2$
On taking square roots of both sides, we get:
$$\begin{gathered} 13=\sqrt{2}\mathrm{AB} \\ \Rightarrow \mathrm{AB}=\frac{13}{\sqrt{2}} \\ =\frac{13\sqrt{2}}{2}\mathrm{cm} \end{gathered}$$
Thus, the length of each side of the square is $\frac{13\sqrt{2}}{2}\mathrm{cm}$.