Answer:
8
Step-by-step explanation:
Use the right triangle altitude theorem. The three triangles are right triangles and are similar.
MP/FP = FP/EP
MP/12 = 12/(EM + MP)
MP/12 = 12/(10 + MP)
MP(10 + MP) = 144
MP^2 + 10MP - 144 = 0
(MP + 18)(MP - 8) = 0
MP = -18 or MP = 8
Since a side length cannot be negative, the answer is MP = 8
Answer: 8
