Answer: Let's call the length of one side of the equilateral triangle x.
Then, the height of the triangle can be represented as √3/2.
By the Pythagorean theorem, we have:
(x/2)^2 + (√3/2)^2 = (x/2)^2 + 3/4 = x^2/4 + 3/4 = x^2/4 + 3/4 = x^2/4
So:
x^2 = 4 * (x^2/4 + 3/4) = 4x^2/4 + 4 * 3/4 = 4x^2/4 + 3
Solving for x:
3x^2/4 = 3
x^2 = 4
x = 2
So the length of one side of the equilateral triangle is 2 feet.
Explanation: