Question

The length of the diagonal of a rhombus is 24 cm. If the side of the Rhombus is 13 cm, find the length of the other diagonal.

Answer 1

Let the rhombus be ABCD, Let the intersecting point of the diagonals be O

Given,

AB=BC=CD=AC=13cm

AC=24cm

Since the diagonals of a rhombus bisect each other at right angles a right triangle BOC is formed.

According to the Pythagoras Theorem,

(BO)²+(CO)²=(BC)²

Since the diagonals bisect each other CO=CA/2

=24cm/2=12cm

Therefore,
(BO)²+(CO)²=(BC)²
(BO)²=(BC)² - (CO)²
(BO)²=(13cm)² - (12cm)²
(BO)²=(169-144)cm

BO=sqrt(25)cm
=5cm

Therefore its other diagonal is (5cm*2)

ie.10cm long