Question

A piece of wire x inches long is bent into the shape of an equilateral triangle. Find a function that represents the area of the triangle and state the domain of the function.

Answer 1

each side will be x/3 inches

sketch a height to create a 30-60-90° triangle
let the height be h
by ratios:
h/(x/3) = √3/2
h = (x/3)(√3/2) = (√3/6)x

area = (1/2)(base)(height)
= (1/2)(x/3)(√3/6)x
= (√3/36)x^2

check my arithmetic

or
h/(x/3) = sin60 = √3/2
h = ..... same as above