1. **Stating the problem:** We have a rectangle cut along a dotted line forming two parts, P and Q. We want to find how the perimeter of Q relates to the perimeter of P. 2. **Understanding the cut:** The cut removes a triangular notch from part P and creates part Q as that notch. The original rectangle's perimeter is unchanged. 3. **Key insight:** The cut line is shared between P and Q. This line is counted once in P's perimeter and once in Q's perimeter. 4. **Perimeter relation:** The sum of the perimeters of P and Q equals the perimeter of the original rectangle plus twice the length of the cut line (because the cut line is counted in both P and Q). 5. **Formula:** Let $P_R$ be the original rectangle perimeter, $P_P$ the perimeter of P, $P_Q$ the perimeter of Q, and $L$ the length of the cut line. $$P_P + P_Q = P_R + 2L$$ 6. **Conclusion:** The perimeter of Q is related to the perimeter of P by the equation above, showing that the sum of their perimeters exceeds the original rectangle's perimeter by twice the cut length. This means the perimeter of Q is not simply equal or proportional to P's perimeter but depends on the cut length and original perimeter.