This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To construct a triangle, the sum of the lengths of any two sides must be greater than the length of the third side (Triangle Inequality Theorem). Given side lengths: PQ = 3.3 cm QR = 4.6 cm PR = 8.2 cm Step 1: Check the Triangle Inequality Theorem. We need to check if PQ + QR > PR, PQ + PR > QR, and QR + PR > PQ. Check 1: PQ + QR > PR 3.3 cm + 4.6 cm = 7.9 cm Is 7.9 cm > 8.2 cm? No, 7.9 cm is not greater than 8.2 cm. Since the first condition of the Triangle Inequality Theorem is not met (7.9 cm 8.2 cm), a triangle with these side lengths cannot be constructed. Therefore, it is impossible to construct PQR with the given side lengths. Consequently, the angles of such a triangle cannot be measured. The triangle cannot be constructed because the sum of the lengths of sides PQ and QR is less than the length of side PR. Send me the next one 📸