SOLUTION: What is the side lengths of an equilateral triangle, whose area is 16 sqrt(3)cm^2 ?

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Question 850109: What is the side lengths of an equilateral triangle, whose area is 16 sqrt(3)cm^2 ?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The altitude of an equilateral triangle divides it into 2 congruent right triangles.

In those right triangles, the hypotenuse is a side of the equilateral triangle; one leg is half of another side of the right triangle, and the other leg is the altitude of the right triangle.
That altitude is also the altitude of the equilateral triangle.
We need to calculate the length of that altitude (the height of the equilateral triangle).
x= side length, in cm.
x%2F2= short leg of the right triangle, in cm.
= height of the right triangle, in cm.

The area of any triangle is calculated as
Area=%28base%2Aheight%29%2F2
For our equilateral triangle,
Area=16%2Asqrt%283%29%7D%7D%7B%7B%7Bcm%5E so
16sqrt%283%29=x%2A%28x%2Asqrt%283%29%2F2%29%2F2
16sqrt%283%29=x%5E2%2Asqrt%283%29%2F4
4%2A16=x%5E2
64=x%5E2
highlight%28x=8%29