Question

5) Lengths of diagonals of a rhombus PQRS are 8 cm and 6 cm. Find the side and perimeter
of the rhombus.​

Answer 1

Answer:

The diagonals of a rhombus bisect each other at 90°.

=> Height = (8/2) cm = 4 cm

=> Base = (6/2) cm = 3 cm

According to Pythagoras Theorem,

(Hypotenuse)² = (Base)² + (Height)²

=> (Hypotenuse)² = (3)² + (4)²

=> (Hypotenuse)² = 9 + 16

=> (Hypotenuse)² = 25

=> Hypotenuse = 5

Therefore, side of rhombus = 5 cm

Perimeter = 4 × side = (4×5) cm = 20 cm