Question

The ratio of adjacent sides of the parallelogram is 2 ∶ 3, and the angle between them is 30°. If the area of the parallelogram is 432 cm². Then find the adjacent sides?
1. 12 cm and 18 cm
2. 18 cm and 27 cm
3. 24 cm and 36 cm
4. 14 cm and 21 cm

Answer 1

Correct Answer - Option 3 : 24 cm and 36 cm

Given:

The ratio of adjacent sides of the parallelogram = 2 ∶ 3

The angle between adjacent sides, θ = 30°

Area of parallelogram = 432 cm²

Concept used:

Area of parallelogram = Product of adjacent sides × Sinθ

Calculation:

Let the adjacent sides are 2x and 3x respectively.

Area of parallelogram = Product of adjacent sides × Sinθ

⇒ 432 = 2x × 3x × Sin30°

⇒ 432 = 6x² × 1/2

⇒ 6x² = 864

⇒ x² = 144

⇒ x = 12

Adjacent sides are:

2x = 24 cm

3x = 36 cm

∴ The adjacent sides of parallelogram is 24 cm and 36 cm.