Question

The side of a rhombus is 13 cm and the length of a diagonal is 24 cm.find the length of 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)

= 10cm long