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