Question

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

Answer 1

The perimeter `=60sqrt3` 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`

`sqrt3/2 xxa = 30`

`a = 30 xx 2/ sqrt3`

`a = 60/ sqrt3`

Rationalising the denominator.

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

`a = (60 sqrt3)/ (3`

`a = 20 sqrt3`

The side, `a = 20 sqrt3` inches.

The perimeter of an equailateral triangle `= 3 xx a` (side)

`= 3 xx 20 sqrt3= 60sqrt3` inches.