Question

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

Answer 1

Here, $ABCD$ is a square.

All sides of the square are equal.

Let $AB=BC=CD=AD=acm$

$AC=13cm$ [ Given ]

In right-angled $△ABC,$

$\Rightarrow$ $(AC{)}^2=(AB{)}^2+(BC{)}^2$ [ By Pythagoras theorem ]

$\Rightarrow$ $(13{)}^2=a^2+a^2$

$\Rightarrow$ $(13{)}^2=2a^2$

$\Rightarrow$ $a^2=\frac{(13{)}^2}{2}$

$\Rightarrow$ $a=\frac{13}{\sqrt{2}}$ [ Taking square root on both sides ]

$\Rightarrow$ $a=\frac{13\times \sqrt{2}}{\sqrt{2}\times \sqrt{2}}$

$\therefore$ $a=\frac{13\sqrt{2}}{2}cm$