Question

Find the length of diagonal of a square with side $8cm.$

Answer 1

Suppose $ABCD$ is a square of side $8cm.$

Here, segment $AC$ is a diagonal of square $ABCD.$
In $△ABC,$ we have
$(AC{)}^2=(AB{)}^2+(BC{)}^2$ (Pythagoras theorem)
$\Rightarrow (AC{)}^2=(8{)}^2+(8{)}^2$
$\Rightarrow (AC{)}^2=64+64=128$
$\Rightarrow \left(AC\right)=\sqrt{128}=\sqrt{8\times 8\times 2}=8\sqrt{2}cm$
Thus, the length of the diagonal of square is $8\sqrt{2}cm.$