SOLUTION: What is the exact perimeter of an equilateral triangle that has a height of 18 cm.

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Question 939987: What is the exact perimeter of an equilateral triangle that has a height of 18 cm.
Answer by MathLover1(20849) About Me  (Show Source):
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An equilateral triangle has 3 equal sides.
If each side is a and a height is h, we know that h divides equilateral triangle into two right triangles with legs h and a%2F2, and hypotenuse a.
use Pythagoras theorem to find a when h=18cm
a%5E2=%28a%2F2%29%5E2%2Bh%5E2
a%5E2-%28a%2F2%29%5E2=%2818cm%29%5E2

a%5E2-a%5E2%2F4=324cm%5E2

4a%5E2%2F4-a%5E2%2F4=324cm%5E2

3a%5E2%2F4=324cm%5E2

3a%5E2=1296cm%5E2

a%5E2=1296cm%5E2%2F3

a%5E2=432cm%5E2

a=sqrt%28432cm%5E2%29
a=sqrt%283%2A144cm%5E2%29
a=12sqrt%283%29cm

then the exact perimeter is:
P=3a
P=3%2A12sqrt%283%29cm
P=36sqrt%283%29cm