Question

Find the side and perimeter of a square whose diagonal is 10 cm.

Answer 1

It is given that ABCD is a square.

∴ AB = BC = CD = DA = a (say)

According to Pythagoras theorem, in ∆ABD

$$\begin{gathered} {\mathrm{AB}}^2+{\mathrm{AD}}^2={\mathrm{BD}}^2 \\ \Rightarrow a^2+a^2={10}^2 \\ \Rightarrow 2a^2=100 \\ \Rightarrow a^2=50 \\ \Rightarrow a=\sqrt{50} \\ \Rightarrow a=5\sqrt{2}\mathrm{cm} \end{gathered}$$

Hence, the side of the square is 5$\sqrt{2}$ cm.

Now,
Perimeter of a square = $4\times \left(\mathrm{side}\right)$
= $4\times a$
= $4\times 5\sqrt{2}$
= $20\sqrt{2}$ cm

Hence, the perimeter of the square is 20$\sqrt{2}$ cm.