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: Find the length of side PR using the given perimeter of PQR. The perimeter of PQR is the sum of its sides PQ, QR, and PR. Given PQ = 6 cm, QR = 8 cm, and the perimeter of PQR = 24 cm. PQ + QR + PR = Perimeter of PQR 6 cm + 8 cm + PR = 24 cm 14 cm + PR = 24 cm Subtract 14 cm from both sides: PR = 24 cm - 14 cm PR = 10 cm Step 2: Calculate the area of PRS. The area of a triangle is given by the formula: Area = (1)/(2) × base × height For PRS, we can consider PR as the base. From the diagram, the perpendicular height from vertex S to the base PR is given as 3 cm. Base (PR) = 10 cm Height = 3 cm Area of PRS = (1)/(2) × PR × height Area of PRS = (1)/(2) × 10 cm × 3 cm Area of PRS = 5 cm × 3 cm Area of PRS = 15 cm^2 The area of PRS is 15 cm^2.