Question

Find the length of the diagonal of a rectangle 12 cm long and 7 cm broad.

Answer 1

The length and breadth of the rectangle are 12 cm and 7 cm, respectively.

Consider ABCD with sides AB = CD = 12 cm, BC = DA = 7 cm .

As all the angles of a rectangle 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
= (12)² + (7)²
= 144 + 49
= 193

Hence, the square of the length of seg BD is 193
It means that the length of seg BD is equal to the square root of 193
In symbols, $\left[l\left(\mathrm{BD}\right)\right]=\sqrt{193}\mathrm{cm}$.