Question

The area A of an equilateral triangle is a function of the length of one of its sides x. Find the formula for the given function and find the domain.

Answer 1

so here, our independent variable is length of one of an equilateral triangle. Let x= length of one side, then height of the equilateral triangle would be h=xsin60.
area is length * height * 1/2
A=x*(xsin60)*1/2= (x^2)sin60/2 =(sqrt3)x^2/4

Answer 2

domain is that length of the equilateral sides is of real numbers, greater than 0.

Answer 3

why did you use a sin(60)?

Answer 4

I was thinking more along the lines of:
A(x) = 1/2 b * h
A(x) = 1/2 x * h
A(x) = 1/2 x * sqrt[ x^2 - (x/2)^2]
A(x) = 1/2 x * sqrt[x^2 - (x^2)/4]
...

Answer 5

that is the same thing.