Final answer:
To solve for the value of P in the geometry problem, we use the information that T and V are midpoints to establish that TV is half of WX. With the relationship of 2P = P + 47, we derive that P equals 47 units.
Step-by-step explanation:
The question presents a geometry problem involving midpoints and line segments. Since T is the midpoint of UX, and V is the midpoint of UW, we can deduce that UT = TX and VW = WU. The distance TV is actually part of both segments UTX and VWU, which implies TV = UT + TV = VW. Because WX is given as P + 47 and TV is given as P, and since TV is half of the entire segment WX, we can set up the equation 2P = P + 47 where P represents the length of segment TV.
To find the value of P, we need to solve the equation. Subtracting P from both sides of the equation to isolate P, we get P = 47. Therefore, the length of the segment TV is 47 units.