Question

The sides of a triangle are in the ratio of 4 ∶ 6 ∶ 3. The perimeter of the given triangle is 52 cm. What is the area of the triangle?
1. 8√65 cm2
2. 16√13 cm2
3. 26√5 cm2
4. 4√455 cm2

Answer 1

Correct Answer - Option 4 : 4√455 cm2

Given:

Ratio of sides of triangle = 4 ∶ 6 ∶ 3

Perimeter of the triangle = 52 cm

Formula used:

Perimeter of triangle = Sum of sides of triangle

Area of triangle = \(√{s(s − a)(s − b)(s − c)}\)

s = (a + b + c)/2​

Calculation:

Let the sides of the triangle be 4x, 6x, and 3x

⇒ 4x + 6x + 3x = 52

⇒ 13x = 52

⇒ x = 4

Sides of triangle = 16 cm, 24 cm, and 12 cm

s = Perimeter/2

⇒ s = 52/2

⇒ s = 26 cm

Area of triangle = \(√{26(26 − 16)(26 − 24)(26 − 12)}\)

⇒ √(26 × 10 × 2 × 14)

⇒ √(7280)

⇒ 4√455 cm²

∴ The area of the triangle is 4√455 cm²