Question

The length of the sides of a triangle is in the ratio 3 : 4 : 5 and its perimeter is 144 cm. The area of the triangle is -

1. 684 cm²
2. 664 cm²
3. 764 cm²
4. 864 cm²

Answer 1

Correct Answer - Option 4 : 864 cm²

Given:

The length of the sides of a triangle is in the ratio 3 : 4 : 5.

The perimeter of triangle is 144 cm.

Formula Used:

Perimeter = Sum of all sides

Area of right-angled triangle = 1/2 × Base × Height

Calculation:

Let the sides of the triangle be 3x, 4x, 5x.

The perimeter of triangle is 144 cm.

⇒ 3x + 4x + 5x = 144

⇒ 12x = 144

⇒ x = 12 cm

The sides = 3 × 12 = 36, 4 × 12 = 48, 5 × 12 = 60

The length of the sides of a triangle is in the ratio 3 : 4 : 5.

It show that the triangle is right angled triangle

Area of triangle = 1/2 × 36 × 48 = 864 cm²

∴ The area of the triangle is 864 cm2