Question

What is the perimeter of an equilateral triangle if the length of an altitude is 5/sqrt3?

Answer 1

Perimeter is 10

`color(red)("Using ratios is a very powerful tool!")`

Explanation:

Let the height of the standardises triangle by `h`
Let the side length of the triangle in the question be `x`

The by ratio of side lengths we have:

`color(blue)(("height of target triangle")/("height of standard triangle")= ("side of target triangle")/("side of standard triangle"))`

`(5/sqrt(3))/h = x/2`

`5/sqrt(3)xx1/h=x/2`

But `h= sqrt(3)` giving

`5/sqrt(3)xx1/sqrt(3) =x/2`

`x=(2xx5)/3`

But this is the length for only one side. There are three sides so:

Perimeter = `(3xx2xx5)/3 = 3/3 xx2xx5=10`