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

1 Answer
Apr 1, 2018

30sqrt3=51.9615 meters

Explanation:

In an equilateral triangle, all sides are equal and all angles are 60 degrees. This means that if you cut the triangle in half by the altitude(also the height in an equilateral triangle), you get 2 30-60-90 triangles(those are the angle measures). These triangles have the relationship:
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The 15 meter height is the xsqrt3 side. To find x, divide by sqrt3.

15/sqrt3*sqrt3 => (15sqrt3)/3=5sqrt3

x=5sqrt3, so 2x=10sqrt3

That is one side of the equilateral triangle, and 10sqrt3*3=30sqrt3.

That is the perimeter.