Question

The diagonals of a rhombus are of lengths 16 centimetres and 12 centimetres. What is its perimeter?

Answer 1

Let the given rhombus be ABCD whose diagonals intersect at a point O.

Given: Diagonal BD = 16 cm and diagonal AC = 12 cm

The figure for the given information can be drawn as follows:

We know that the diagonals of a rhombus are perpendicular bisectors of each other.

∴ BO =

OC =

Also, ∠BOC = 90°

In ΔBOC, using Pythagoras theorem, we get:

Since all the sides of a rhombus are equal in length, AB = BC = CD = DA = 10 cm.

Perimeter of the rhombus = 4 × AB

= 4 × 10 cm

= 40 cm