Question

Area of a rhombus is 384 cm² and one of its diagonal is 24 cm then find its altitudes.

1. 19.2 cm
2. 20 cm
3. 20.2 cm
4. 21 cm

Answer 1

Correct Answer - Option 1 : 19.2 cm

Given:

Area of Rhombus = 384 cm2

Diagonal, (d1) = 24 cm

Formula used:

Area of Rhombus = (d1 × d2)/2

Area of Rhombus = Side × Altitude

d12 + d22 = 4 × s2

Here, d1, d2, and s are diagonals and side of rhombus respectively.

Concept used:

All sides of a rhombus are equal and diagonals bisect each other at a right angle.

Calculation:

Let diagonal 2 be d2 and side be s

Area of Rhombus = (d1 × d2)/2 = Side × Altitude

384 = (24 × d2)/2

⇒ d2 = 384/12

⇒ d2 = 32

Now, d12 + d22 = 4 × s2

⇒ 242 + 322 = 4 × s2

⇒ s2 = 400

⇒ s = 20

Now, Area of Rhombus = Side × Altitude

384 = 20 × Altitude

⇒ Altitude = 19.2

∴ The Altitude of rhombus is 19.2 cm