1. **Problem Statement:** We are given a quadrilateral PNOR with two triangles PQR and QRO inside it. The lengths are QN = 8.2, RO = 10.9, and PQ = 9.8. We need to find the length of PR. 2. **Understanding the Problem:** Since PR is a diagonal crossing the quadrilateral, and points Q and R are inside the figure, we can use the triangle inequality or properties of triangles to find PR. 3. **Using the Triangle Inequality:** In triangle PQR, the length PR must satisfy: $$|PQ - QR| < PR < PQ + QR$$ But we don't have QR directly. However, since QN and RO are given, and assuming QN and RO are parts of segments related to QR, we need more information or assumptions. 4. **Assuming QN and RO are segments along QR:** If QN and RO are parts of QR, then: $$QR = QN + RO = 8.2 + 10.9 = 19.1$$ 5. **Calculate PR using triangle PQR:** Now, with PQ = 9.8 and QR = 19.1, apply the Law of Cosines if angle is known or use the triangle inequality to estimate PR. 6. **If angle is unknown, approximate PR:** Since no angle is given, the best estimate is the sum or difference: $$|9.8 - 19.1| < PR < 9.8 + 19.1$$ $$9.3 < PR < 28.9$$ 7. **If PR is the diagonal connecting P and R, and assuming P, Q, R are collinear or nearly so, PR could be approximated as: $$PR = PQ + QR = 9.8 + 19.1 = 28.9$$ 8. **Final answer:** Without more information, the best estimate for PR is 28.9, rounded to the nearest tenth. **Answer:** $PR = 28.9$