Triangle EFG is a right angled triangle (right angled at ∠EGF) with EG = 7, FG = 24.

Point P is the midpoint of EF, and:

H is on the same side of line EF as G so that EH = FH = 15, and:

The area of triangle GHP is expressible as x*√y/z, where each of x, y and z is a positive integer, and:

x and z are relatively prime, and y is not divisible by the square of any prime.

Determine x, y and z