Question

The diagonal of a rectangle is 65 centimetres long and one of its sides is 63 centimeres long. What is the length of the other side?

Answer 1

Given: A rectangle ABCD with length of one side, DC = 63 cm and length of the diagonal, BD = 65 cm.

We know that each angle of a rectangle measures 90°.

In ΔBCD, ∠BCD = 90°

Using Pythagoras theorem, we get:

BD² = BC² + CD²

⇒ (65)² = BC² + (63)²

⇒ BC² = (65)² − (63)²

= (65 − 63) (65 + 63) {x² − y² = (x − y) (x + y)}

= 2 × 128

= 256

⇒ BC = 16

Thus, the length of the other side of the rectangle is 16 cm.