SOLUTION: the altitude of an equilateral triangle is 12 centimeters. Find the perimeter of the triangle. Round to the nearest tenth.

Algebra ->  Triangles -> SOLUTION: the altitude of an equilateral triangle is 12 centimeters. Find the perimeter of the triangle. Round to the nearest tenth.      Log On


   

Question 181165: the altitude of an equilateral triangle is 12 centimeters. Find the perimeter of the triangle. Round to the nearest tenth.
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
Formula: If a triangle is equilateral of side s, then the altitude is %28s+sqrt%283%29%29%2F2
Here, the altitude is given as 12 cm.
Let s=side of the triangle.
Then,
%28ssqrt%283%29%29%2F2=12
ssqrt%283%29=24
s=24%2Fsqrt%283%29
This is not the answer yet. We have to rationalize the denominator. Let's multiply the right side by sqrt%283%29%2Fsqrt%283%29
s=%2824%2Fsqrt%283%29%29%28sqrt%283%29%2Fsqrt%283%29%29=%2824sqrt%283%29%29%2F3=8sqrt%283%29
The equilaterla triangle has three congruent sides. Therefore, the perimeter,
P=3%288sqrt%283%29%29=24sqrt%283%29cm
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