SOLUTION: If an equilateral triangle has an area of 4, what is the length of a side in radical form?

Question 273242: If an equilateral triangle has an area of 4, what is the length of a side in radical form?
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
If an equilateral triangle has an area of 4, what is the length of a side in radical form?
pythagorean theorem (1/2 the equilateral triangle) --> L^2 = (L/2)^2 + H^2
L^2 = L^2/4 + H^2
3L^2/4 = H^2
(sqrt(3) * L)/2 = H
3L^2 = 4H^2
L^2 = 4/3 * H^2
L = 2/sqrt(3) * H
area = 4 = 1/2 * (2/sqrt(3) * H) * H
4 = 1/sqrt(3) * H^2
4sqrt(3) = H^2
2*3^(1/4) = H
L = 2* 3^(-2/4) * 2 * 3^(1/4) = 4*3^(-1/4) (3^(-2/4) = 3^(-1/2) = 1/sqrt(3))
check: A = 1/2 * 4*3^(-1/4) * 2 * 3^(1/4) = 4 * 3^(-1/4) * 3^(1/4) = 4 * 1 = 4

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