How do you calculate the length of a side of an equilateral triangle given the height?

Letting S represent the length of a side of an equilateral triangle having a height of 1 unit, then drawing a perpendicular from the mid point of a side to the opposite vertex creates a right triangle having sides 1, S, and ½S, with S being the hypotenuse of a right triangle. The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides; thus S2 = (H2 + (½)2S2) = 1 + ¼S2. Subtracting 1 from each side, S2 - 1 = ¼S2. Multiplying the terms on each side by 4, 4S2 - 4 = S2; subtracting S2 from each side, 3S2 - 4 = 0; adding 4 to each side, 3S2 = 4; dividing each side by 3, S2 = 4/3; Taking the square root of each side, S = 2/1.732 = 1.1547 The length of each side of an equilateral triangle is the product of 1.1547 x height. (Note: 1.1547 is twice the reciprocal of the square root of 3.) Example: if the height of an equilateral triangle is 30 cm, the length of each side will be 34.641cm (30 x 1.1547cm).