Question 273242
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