Question

If side of a square = 4 cm, then the length of its diagonal =

• A. 4cm
• B. 4$\sqrt{2}$ cm
• C. 4$\sqrt{3}$ cm
• D. 5cm

Answer 1

The correct option is B 4$\sqrt{2}$ cm

Given: side of the square = 4 cm.

Since a square is a regular quadrilateral, all its sides are equal. Also each side makes a right angle with the adjacent side.

$\therefore$ AB = BC = CD = DA= 4 cm

In $△$ ABC, using Pythagoras theorem

${AB}^2$+ ${BC}^2$= ${AC}^2$

$4^2$+ $4^2$= ${AC}^2$

2 × $4^2$= ${AC}^2$ = AC = 4$\sqrt{2}$ cm

We know both diagonals in a square are equal in length. AC = BD = 4$\sqrt{2}$ cm