Question

If the diagonal of rhombus are 8cm and 6cm,Find it’s perimeter.

Answer 1

Answer:

The perimeter of the rhombus is 20 cm.

Step-by-step explanation:

Refer to the diagram attached.

Let ABCD be a rhombus.

Given the length of diagonals = 8 cm and 6 cm

Let AD = 8 cm and BC = 6 cm

We know that the diagonals of a rhombus bisect at right angles,

Therefore,

• AO = OD = 4cm and BO = OC = 3 cm
• ∠AOC = ∠AOB = ∠BOD = ∠DOC = 90°

Therefore, in Δ AOC, using Pythagoras Theorem,

(AO)² + (OC)² = (AC)²

=> 4² + 3² = (AC)²

=> 16 + 9 = (AC)²

=> 25 = (AC)²

=>  AC = ±5

Since, length cannot be negative, AC = 5 cm

We know that in a rhombus, all the sides are equal.

Therefore, the perimeter of rhombus = 4 * Length of 1 side

=> Perimeter = 4 * AC

                     = 4 * 5

                     = 20 cm

Therefore, the perimeter of the rhombus is 20 cm.