# An equilateral triangle has an altitude that measures 6√3 cm. What is the perimeter of this triangle?

Question
An equilateral triangle has an altitude that measures 6√3 cm. What is the perimeter of this triangle?

2021-02-15
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

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