# An altitude of an equilateral triangle is 30 inches. How do you find the perimeter of the triangle?

Mar 4, 2016

The perimeter $= 60 \sqrt{3}$ inches.

#### Explanation:

The formula for the altitude of an equilateral triangle is:
color(blue)(sqrt3/2 xx  (side)

The altitude of the equilateral triangle is $30$ inches.
Let the side of the triangle be denoted as $a$

$\frac{\sqrt{3}}{2} \times a = 30$

$a = 30 \times \frac{2}{\sqrt{3}}$

$a = \frac{60}{\sqrt{3}}$

Rationalising the denominator.

a = (60 xx sqrt3)/ (sqrt3 xx sqrt3

a = (60 sqrt3)/ (3

$a = 20 \sqrt{3}$

The side, $a = 20 \sqrt{3}$ inches.

The perimeter of an equailateral triangle $= 3 \times a$ (side)

$= 3 \times 20 \sqrt{3} = 60 \sqrt{3}$ inches.