Question

An equilateral triangle has an altitude of 15 m. What is the perimeter of the triangle?

Answer 1

we know that

In the equilateral triangle every sides and angles are equal 

so

the measure of internal angles is equal to $60$ degrees 

see the attached picture to better understand the problem

In the right triangle ABC

$sin 60=BC/AB$

where

BC is the altitude (opposite side angle $60$ degrees

AB is the hypotenuse

Clear AB

$AB=BC/sin 60\\ AB=15/(\frac{\sqrt{3}}{2} )\\ AB=30/\sqrt{3}m$

Perimeter of the triangle is equal to

$P=AB+BD+AD$

but remember that

$AB=BD=AD$

so

$P=3*AB\\ P=3*\frac{30}{\sqrt{3}} \\ \\ P=\frac{90}{\sqrt{3}} \\ \\ P=30\sqrt{3} m$

therefore

the answer is

$30\sqrt{3} m$

Answer 2

Equilateral triangle mean every sides and angles are equal 
so the measure of angles is 60 degrees 
 given that has an altitude of 15 m so this mean that 

sin 60 = altitude / hypotenuse 

sqrt3 /2 = 15/hyp.

hyp. = 15/(sqrt3 /2)

hyp. = 30/sqrt3 = 30sqrt3 / 3 = 10sqrt3

so in this way ve got that a side length is equal 10sqrt3 and the perimeter 

P = 3*10sqrt3 

P = 30sqrt3 m  so the 3rd choice is right,correct sure 

hope helped