Question

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

• A. Length of diagonals
• B. Length of each side
• C. Each angle is 60${}^0$
• D. Can determine both the length of the diagonal and length of each side

Answer 1

The correct option is D Can determine both the length of the diagonal and length of each side

Since a square is regular quadrilateral all of its sides are equal to each other

AB = BC = CD = DA= 4cm

So, 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

So we also know the length of the diagonals.