Question 12
The set of points in $3$-dimensional coordinate space that lie in the plane $x + y + z = 75$ whose coordinates satisfy the inequalities $$
x - yz \lt y - zx \lt z - xy
$$ forms 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 $a + b.$
x - yz \lt y - zx \lt z - xy
$$ forms 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 $a + b.$