Question

The diagonal of a square is $12cm$ long. find its area and length of one side.

Answer 1

Let side of square be $acm$, diagonal $=12cm$

By Pythagoras Theorem,

$a^2+a^2=(12{)}^2$

$\Rightarrow 2a^2=144$

$\Rightarrow a^2=72$

$\therefore$ Area of square $=a^2$ $=72c{m}^2$

$a^2=72$

$\Rightarrow a=\sqrt{72}=8.49cm$

Hence, area of the square is $72c{m}^2$ and the length of the one side is $8.49cm$.