Question

What is the perimeter of a 30-60-90 triangle with a shortest side of 3?

Answer 1

3
`√(3)` + 9

Explanation:

In a 30-60-90 triangle, the hypotenuse is twice the short leg.

In this case the hypotenuse is 2*3 = 6 units long.

In a 30-60-90 triangle, the long side is
`√(3)` times as long compared to the short side.

So:

long side = short side *
`√(3\\)`

long side = 3 *
`√(3)` = 3
`√(3)`

Perimeter = long side + short side + hypotenuse

Perimeter = 3
`√(3)` + 3 + 6

Perimeter = 3
`√(3)` + 9