An equilateral triangle's altitude is v15 - what's the length & perimeter?

Question

I came across this problem and got very stuck. I'd appreciate a response from you.

Answer 1

Note:  In any 30-60-90 triangle, 

 

          if x = length of shortest side (side opposite 30° angle)

 

          then 2x = length of hypotenuse

 

            and x√3 = length of side opposite 60° angle

 

The altitude is the side opposite the 60° angle of a 30-60-90 triangle.

 

So, x√3 = √15

 

         x = √5

 

      2x = 2√5 = hypotenuse

 

                    = length of one side of the equilateral triangle

 

Perimeter = 3(2√5) = 6√5