The sides of a parallelogram are 3x + 2 and 5x + 4. It has a perimeter of 44 cm and an area of 64 cm². The value of the acute angle between its sides in degrees is:

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Question

This question was previously asked in

NTPC CBT-I (Held On: 13 Jan 2021 Shift 1)

Answer 1

Given:

Sides of a parallelogram = 3x + 2 and 5x + 4

Perimeter = 44 cm and area = 64 cm²

Formula Used:

Perimeter of parallelogram = 2 (side + base)

Solution:

⇒ Perimeter = 2(3x + 2) + 2(5x + 4)

⇒ 44 = 2(3x + 2) + 2(5x + 4)

⇒ 44 = 6x + 4 + 10x + 8

⇒ 16x = 32

⇒ x = 2

Therefore the sides of parallelogram are,

⇒ 3x + 2 = 8

⇒ 5x + 4 = 14

Area of triangle = 1/2 × Area of parallelogram

⇒ 1 / 2 × 8 × 14 × sinθ = 64 / 2

⇒ sinθ = 0.571

We know that, sin 30° = 1/2 = 0.5 and sin 60° = √3 / 2 = 1.73/2 = 0.865

Also, the value of sin increases till 90° and decreases thereafter.

Hence option 4 is correct.