Question

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

• A. $4$ cm
• B. $16$ cm
• C. $8$ cm
• D. $16\sqrt{2}$ cm

Answer 1

Answer: (B)

$16$ cm

We know that,

1) All angles of a square are congruent. i.e ${90}^o$

2) Diagonal of a square bisects each of its angles.

Therefore, the square gets divided into $2$ triangles of degrees ${45}^o-{45}^o-{90}^o$

$\therefore \sin {45}^o=\frac{\text{side}}{\text{hyp}}$

$\therefore \frac{1}{\sqrt{2}}=\frac{\text{side}}{16\sqrt{2}}$

$\therefore$ side of the square $=16$ cm.