Question

If you know that side of a square is 4 cm, you also know:

• A. Length of diagonals
• B. Length of each side
• C. Length of diagonals and the length of each side
• D. Only the length of the given side

Answer 1

The correct option is C

Length of diagonals and the length of each side

Given, side of a square is 4 cm.

Since a square is regular quadrilateral all of its sides are equal to each other and each side makes a right angle with the corresponding side.

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

So, the length of every side is known.

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

So, we know the length of the diagonals since in square, both diagonals are equal in length AC = BD = 4$\sqrt{2}$ cm