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
Here's an analysis of the figures provided: a) Triangle ABC This is a right-angled triangle with the right angle at A. We are given the hypotenuse BC = 13 cm and one leg AC = 12 cm. We can find the length of the other leg, AB, using the Pythagorean theorem. Step 1: Apply the Pythagorean theorem. AB^2 + AC^2 = BC^2 Step 2: Substitute the given values. AB^2 + (12 cm)^2 = (13 cm)^2 AB^2 + 144 cm^2 = 169 cm^2 Step 3: Solve for AB. AB^2 = 169 cm^2 - 144 cm^2 AB^2 = 25 cm^2 AB = sqrt(25 cm)^2 AB = 5 cm b) Triangle DEF This is a right-angled triangle with the right angle at E. We are given the lengths of the two legs, DE = 15 cm and EF = 10 cm. We can find the length of the hypotenuse, DF, using the Pythagorean theorem. Step 1: Apply the Pythagorean theorem. DE^2 + EF^2 = DF^2 Step 2: Substitute the given values. (15 cm)^2 + (10 cm)^2 = DF^2 225 cm^2 + 100 cm^2 = DF^2 Step 3: Solve for DF. DF^2 = 325 cm^2 DF = sqrt(325 cm)^2 DF = sqrt(25 × 13 cm)^2 DF = 5sqrt(13) cm c) Quadrilateral ABCD Step 1: Identify the properties of the quadrilateral. The figure shows a quadrilateral with all four angles marked as right angles (90^). The adjacent sides have different lengths (AB = 10 cm and BC = 15 cm). This shape is a rectangle. d) Quadrilateral PQRS Step 1: Identify the properties of the quadrilateral. The figure shows a quadrilateral with all four angles marked as right angles (90^). The adjacent sides have equal lengths (PQ = 10 cm and QR = 10 cm). This shape is a square. Send me the next one 📸