The altitude of an equilateral triangle divides it into two 30°-60°-90° triangles where the hypotenuse is the side of the equilateral triangle and the altitude is the longer leg. In a 30°-60°-90°, the longer leg is √3 times the shorter leg and the hypotenuse is 2 times the shorter leg.

If x is the side (hypotenuse) and y is the shorter leg, we write: x=2y

Also, \(\displaystyle{6}√{3}=√{3}\cdot{y}\)

6=y

Hence, the side length of the equilateral triangle is:

x=2(6)=12 cm

So, its perimeter is: P=3(12)=36 cm

If x is the side (hypotenuse) and y is the shorter leg, we write: x=2y

Also, \(\displaystyle{6}√{3}=√{3}\cdot{y}\)

6=y

Hence, the side length of the equilateral triangle is:

x=2(6)=12 cm

So, its perimeter is: P=3(12)=36 cm