Question

Find the side of a square whose diagonal is 16$\sqrt{2}$ cm.

Answer 1

First, we draw the figure of square ABCD in which the length of diagonal AC is 16$\sqrt{2}$ cm.


We know that the diagonal of a square bisects the angles of the square.
Thus,
$\angle$CAB = $\angle$ACB =$\frac{90°}{2}=45°$ .
Now, in Δ ABC, $\angle$CAB = $\angle$ACB = 45° and $\angle$ABC = 90°.
Thus, Δ ABC is a 45°–45°–90° triangle.
We know that if the angles of the triangle are 45°, 45° and 90°, then each of the perpendicular sides is $\frac{1}{\sqrt{2}}$ times the hypotenuse. Thus,
AB = $\frac{1}{\sqrt{2}}$× AC = $\frac{1}{\sqrt{2}}$× 16$\sqrt{2}$ = 16 cm

Thus, each side of the square is 16 cm long.