Question

The sides of a rhombus are 5 cm each and one diagonal is 8 cm, calculate

1. The length of the other diagonal,
2. The area of the rhombus.

Answer 1

Given: Sides of rhombus = 5 cm, one diagonal d₁ = 8 cm.

Step-wise calculation:

Diagonals of a rhombus bisect each other at right angles, so half-diagonals form a right triangle with a side of the rhombus.

Half of d₁ = `8/2` = 4 cm. Let half of the other diagonal be x cm, so the other diagonal d₂ = 2x.

By Pythagoras on the right triangle:

Side² = (half d₁)² + x² 

⇒ 5² = 4² + x²

⇒ 25 = 16 + x²

⇒ x² = 9

⇒ x = 3 cm

Therefore, the other diagonal d₂ = 2x = 6 cm.

Area of rhombus = `1/2` × product of diagonals 

= `1/2 xx 8 xx 6` 

= 24 cm²

i. Other diagonal = 6 cm.

ii. Area = 24 cm².