1. **Problem Statement:** We are given a triangle $\triangle VXZ$ with $WY$ as a midsegment. The segment $VZ$ has length $p$, and the midsegment $WY$ has length $p - 14$. We need to find the value of $p$. 2. **Key Concept:** A midsegment in a triangle connects the midpoints of two sides and is parallel to the third side. The length of the midsegment is always half the length of the side it is parallel to. 3. **Formula:** If $WY$ is a midsegment parallel to $VZ$, then: $$ WY = \frac{1}{2} VZ $$ 4. **Apply the formula:** Substitute the given lengths: $$ p - 14 = \frac{1}{2} p $$ 5. **Solve for $p$:** Multiply both sides by 2 to clear the fraction: $$ 2(p - 14) = p $$ $$ 2p - 28 = p $$ Subtract $p$ from both sides: $$ 2p - p - 28 = 0 $$ $$ p - 28 = 0 $$ Add 28 to both sides: $$ p = 28 $$ 6. **Answer:** The value of $p$ is 28.