Andrew M. answered • 02/14/18

Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors

If you draw the equilateral triangle... which is 60

^{o}, 60^{o}, 60^{0}Then use the height.. in this case 38 inches to cut the equilateral

triangle into to equal right triangles of 30

^{0}, 60^{0}, 90^{0}Label half the base as x

Label the full side (now the hypotenuse of a right triangle) as 2x

Label the height as 38

x

^{2}+ h^{2}= (2x)^{2}from Pythagorean Theoremx

^{2}- 4x^{2}= -h^{2}-3x

^{2}= -h^{2}x

^{2}= -h^{2}/-3x

^{2}= h^{2}/3x = √(h

^{2}/3)x = h/√3

**Side length = 2x = 2h/√3**

Basically what I have done is worked out the formula for you.

This formula can be used for any height h to find the associated

side lengths for an equilateral triangle.

Side length = 2(38)/√3 = 76/√3 ≅ 43.88 inches