SOLUTION: how do you figure out the side lengths of an equalateral triangle when given the area

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Question 607062: how do you figure out the side lengths of an equalateral triangle when given the area
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
As with any triangle, +A+=+%281%2F2%29%2Ab%2Ah+
Let the sides of the equilateral triangle = s
Now the formula becomes +A+=+%281%2F2%29%2As%2Ah+
Dropping a vertical to the base forms 2 back to back
30-60-90 triangles.
Opposite the 30 is +s%2F2+
Opposite the 60 is +%28s%2F2%29%2Asqrt%283%29+
Opposite the 90 is +s+
The vertical, h, is opposite the 60 degree angle, so
+A+=+%281%2F2%29%2As%2A%28s%2F2%29%2Asqrt%283%29+
+A+=+%28s%5E2%2F4%29%2Asqrt%283%29+
+A+=+%28s%2F2%29%5E2%2Asqrt%283%29+