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
Step 1: Identify the given information and the relevant theorem. The problem describes a triangle PQR where S is the midpoint of PQ and T is the midpoint of PR. The length of ST is given as 4 cm. We need to find the length of QR. This scenario directly applies the Midpoint Theorem. Step 2: State the Midpoint Theorem. The Midpoint Theorem states that the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half the length of the third side. Step 3: Apply the theorem to find QR. According to the Midpoint Theorem, since S and T are midpoints of PQ and PR respectively, the length of ST is half the length of QR. ST = (1)/(2) QR Step 4: Substitute the given value and solve for QR. We are given ST = 4 cm. 4 = (1)/(2) QR To find QR, multiply both sides by 2: QR = 4 × 2 QR = 8 cm The length of QR is: 8 cm Send me the next one 📸