2025 AIME I Problem 12

The set of points in 3-dimensional coordinate space that lie in the plane x+y+z=75 whose coordinates satisfy the inequalities x-yz<y-zx<z-xyforms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form a\sqrt{b}, where a and b are positive integers and b is not divisible by the square of any prime. Find a+b.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.