The length of PX is 71 units.
To find the length of PX, we can use the fact that point P is the circumcenter of triangle AXYZ. The circumcenter is the point where the perpendicular bisectors of the sides intersect.
Given that PY = 5x - 4 and PZ = 4x + 11, we need to find the value of x to determine the length of PX.
To do this, we can set the distances PY and PZ equal to each other, since point P is equidistant from Y and Z:
5x - 4 = 4x + 11
Solving this equation, we find:
x = 15
Now that we know the value of x, we can substitute it back into the given equations to find the lengths of PY and PZ:
PY = 5(15) - 4 = 71
PZ = 4(15) + 11 = 71
Since point P is equidistant from Y and Z, the length of PX is also 71.
Therefore, the length of PX is 71 units.