Question

Find the length of the diagonal of the square with side 8 cm.

Answer 1

The length of the given side of the square is 8 cm.

Consider square ABCD with sides AB = CD = BC = DA = 8 cm
As all the angles of a square are equal, m$\angle$ABC = m$\angle$BCD = m$\angle$CDA = m$\angle$DAB = 90°
So, the length of the diagonal can be found out by Pythagoras theorem.

By Pythagoras theorem,
[l(BD)]² = [l(DC)]² + [l(BC)]²
= (8)² + (8)²
= 64 + 64
= 128
Hence, the square of the length of seg BD is 128
It means that the length of seg BD is equal to the square root of 128
In symbols, $\left[l\left(\mathrm{BD}\right)\right]=\sqrt{128}\mathrm{cm}$