The vertices of an equilateral triangle, with perimeter P and area A, lie on a circle with radius r. Find an expression for P/A in terms of r.

4/r

Step-by-step explanation:

The side lengths s of an equilateral triangle inscribed in a circle of radius r will be ...

s = r√3

The perimeter of the triangle will be 3s.

The area of the triangle will be s^2· (√3) / 4.

Then the ratio P/A is ...

P/A = (3s) / (s^2· (√3) / 4) = (4√3) / s

Substituting the above expression for s, we have ...

P/A = 4√3 / (r√3)

P/A = 4/r