Question

The length of an altitude of an equilateral triangle is √3/2 feet. Find the length of one side of the triangle

Answer 1

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: