Question

The perimeter of a triangle is 72 cm, and the length of the sides are in the ratio 2 ∶ 3 ∶ 4. Find the lengths of the three sides in cm.
1. 34, 24, 18
2. 2, 3, 4
3. 16, 24, 32
4. None of these

Answer 1

Correct Answer - Option 3 : 16, 24, 32

Given:

The perimeter of triangle = 72 cm

Ratio of sides = 2 ∶ 3 ∶ 4 

Formula used:

Perimeter of triangle = a + b + c

Where,

a, b and c are the length of the side of triangle.

Calculation:

Let the length of the sides be 2x, 3x and 4x.

The perimeter of triangle = a + b + c

⇒ 72 = 2x + 3x + 4x

⇒ 72 = 9x

⇒ x = 8

Now,

a = 2x

⇒ a = 16 cm

b = 3x

⇒ b = 24 cm

c = 4x

⇒ c = 32 cm

∴ The length of all three sides are 16 cm, 24 cm and 32 cm.