# Algebraic Geometry

Let ABC be an equilateral triangle with side lengths of \(x\). ABC is inscribed in a circle with some radius. Let \(f\) be a function that describes the relationship between the area of triangle ABC and its side length in terms of \(x\). Let \(g\) be a function that describes the relationship between the side length of ABC and the radius of the circle that it is inscribed in, once again in terms of \(x\). What is \(f+g(24)\) rounded to the nearest whole number?