Question

Find the length of the diagonal of a square of side $12cm$.

Answer 1

Let $ABCD$ be the square and $AC$ be the diagonal as shown in the above figure:

It is given that $AB=BC=CD=DA=12$ cm

In $△ABC$, $\angle B={90}^0$

According to the pythagoras theorem

$A{C}^2=A{B}^2+B{C}^2\Rightarrow A{C}^2={12}^2+{12}^2\Rightarrow A{C}^2=144+144\Rightarrow A{C}^2=288\Rightarrow AC=\sqrt{288}\Rightarrow AC=\sqrt{{12}^2\times 2}\Rightarrow AC=12\sqrt{2}$

Hence, the length of the diagonal is $AC=12\sqrt{2}$ cm.