Find the length of the side of an equilateral triangle that has an altitude length of 11 radical 3 feet

Let x be the length of the side of the equilateral triangle. x will also be the base on which the altitude falls. One side, the altitute and 1/2 the base forms a right triangle. so x² = (x/2) ² + (11√3) ² x² = (x²/4) + (121) (3) x² - (x²/4) = (121) (3) 3x²/4 = (121) (3) x² = (4/3) (121) (3) x² = 4 (121) x = 2 (11) x = 22