# An equilateral triangle has an altitude of 15 m. What is the perimeter of the triangle?

An equilateral triangle is a triangle having all the sides equal and the angle between the sides is 60°. The perimeter is equal to the sum of all sides.

## Answer: The perimeter of the triangle is 30√3 m or 51.96 m.

Let' understand the explanation

**Explanation:**

Given:

Altitude(h) of a triangle = 15 m.

Angle(θ) between the sides = 60° [the measure of each angle of an equilateral triangle is 60°]

We know that the perimeter of the equilateral triangle = 3 × side = 3a

Also the altitude of the equilateral triangle, h = side × (√3)/2

So, side = altitude × (2/√3)

a = 15 × 2/√3

a = 30 /√3 m

Now,

Perimeter = 3a

= 3 × 30 /√3

= 90/√3

= (90/√3) × (√3/√3) [rationalization]

= 30√3 m = 51.96 m