Question

If the side of the square is $7\text{cm}$, what will be the length of its diagonal?

• A. $7\sqrt{2}\text{cm}$
• B. $2\sqrt{7}\text{cm}$
• C. $14\text{cm}$
• D. $7\sqrt{2}\text{cm}$

Answer 1

The correct option is A $7\sqrt{2}\text{cm}$

Let the given square be represented as,


Here $ABCD$ is a square with a diagonal $AC$.

We know that the sides of a square makes an angle of ${90}^{\circ }$, therefore apply the Pythagoras theorem in $△ABC$, to find the length of diagonal.

The $△ABC$ can be depicted as,


On applying Pythagoras theorem, we get

$\begin{array}{cc}A{C}^2& =A{B}^2+B{C}^2\\ & =7^2+7^2\\ & =49+49\\ & =98\\ \therefore AC& =\pm \sqrt{98}\\ & =\pm 7\sqrt{2}\end{array}$

Since the length of a diagonal cannot be negative, therefore $AC=7\sqrt{2}$.

Hence, the diagonal of a square of side $7\text{cm}$ is $7\sqrt{2}\text{cm}$.