SOLUTION: how do I find the height of an equilateral triangle that has a perimeter of 24

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Question 1073959: how do I find the height of an equilateral triangle that has a perimeter of 24
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
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Each side is 8 units in length. The equilateral triangle is composed of TWO special 30-60-90 type RIGHT triangles having a leg of 24/2=12 8%2F2=4 and a hypotenuse of 8. The other leg is the altitude of the equilateral triangle. Use Pythagorean Theorem Formula.

Let a be the altitude.
cross%28a%5E2%2B12%5E2=24%5E2%29------Hypotenuse is 8 units in length. This means the short leg is 4 units of length.
a%5E2%2B4%5E2=8%5E2
(solve for a.)


Answer by ikleyn(52781) About Me  (Show Source):
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.
The side length is a = 24%2F3 = 8 units.


The altitude is h = a%2A%28sqrt%283%29%2F2%29 = 8%2A%28sqrt%283%29%2F2%29 = 4%2Asqrt%283%29.


Answer. The altitude length is  4%2Asqrt%283%29.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
how do I find the height of an equilateral triangle that has a perimeter of 24
highlight%28a=12sqrt%283%29%29 <============= INCORRECT/RIDICULOUS/NONSENSICAL answer

Altitude: highlight_green%284sqrt%283%29%29 <======= Correct answer

The altitude will be the LONGER leg of one of two 30-60-90 special right-triangles, formed from the altitude being drawn from one 

of the equilateral triangle's vertices, to its opposite side. Thus, the ALTITUDE/LONGER leg is: matrix%281%2C6%2C+Shorter%2C+leg%2C+%22%2A%22%2C+sqrt%283%29%2C+%22=%22%2C+4sqrt%283%29%29

That's how SIMPLE this problem is.