Question

The area of a rhombus is 480 cm² and the length of one of its diagonals is 20 cm. The length of each side of the rhombus is ______.

Options

• 24 cm

• 30 cm

• 26 cm

• 28 cm

Answer 1

The area of a rhombus is 480 cm² and the length of one of its diagonals is 20 cm. The length of each side of the rhombus is 26 cm.

Explanation:

`1/2 xx d_1 xx d_2 = 480  cm^2`

⇒ `1/2 xx 20  cm xx d_2 = 480  cm^2`

⇒ d₂ = 48 cm

∴ OB = 10 cm, OA = 24 cm and ∠AOB = 90°.

∴ AB² = OA² + OB² 

= [(24)² + (10)²] cm²

= (576 + 100) cm² 

= 676 cm²

⇒ `AB = sqrt(676)  cm`

⇒ AB = 26 cm

Hence, each side of the rhombus is 26 cm.