Question

If the length of the diagonal of a square is 20 cm, then its perimeter is

(a) $10\sqrt{2}\mathrm{cm}$
(b) 40 cm
(c) $40\sqrt{2}\mathrm{cm}$
(d) 200 cm

Answer 1

(c) 40 $\sqrt{2}$cm

Length of the diagonal = 20 cm

Length of the side of a square = $\left(\frac{LengthofDiagonal}{\sqrt{2}}\right)$ = $\frac{20}{\sqrt{2}}$ = $\frac{2\times 10}{\sqrt{2}}$
= $\frac{\sqrt{2}\times \sqrt{2}\times 10}{\sqrt{2}}$ = 10$\sqrt{2}$ cm

Therefore, perimeter of the square = 4 $\times$ Side = 4 $\times$10$\sqrt{2}$ = 40$\sqrt{2}$ cm