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

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

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Answer 1 · 2018-04-01T18:59:27

$30 \sqrt{3} = 51.9615$ $30sqrt3=51.9615$ meters

Explanation:

In an equilateral triangle, all sides are equal and all angles are $60$ $60$ degrees. This means that if you cut the triangle in half by the altitude(also the height in an equilateral triangle), you get $2$ $2$ $30 - 60 - 90$ $30-60-90$ triangles(those are the angle measures). These triangles have the relationship:
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The 15 meter height is the $x \sqrt{3}$ $xsqrt3$ side. To find x, divide by $\sqrt{3}$ $sqrt3$ .

$\frac{15}{\sqrt{3}} \cdot \sqrt{3} \Rightarrow \frac{15 \sqrt{3}}{3} = 5 \sqrt{3}$ $15/sqrt3*sqrt3 => (15sqrt3)/3=5sqrt3$

$x = 5 \sqrt{3}$ $x=5sqrt3$ , so $2 x = 10 \sqrt{3}$ $2x=10sqrt3$

That is one side of the equilateral triangle, and $10 \sqrt{3} \cdot 3 = 30 \sqrt{3}$ $10sqrt3*3=30sqrt3$ .

That is the perimeter.

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

1 Answer

Explanation:

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