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 the hypotenuse (side 'a') using the Pythagorean theorem. The legs of the right-angled triangle are 8 m and 12 m. Let a be the hypotenuse. a^2 = (8 m)^2 + (12 m)^2 a^2 = 64 m^2 + 144 m^2 a^2 = 208 m^2 a = sqrt(208) m To simplify sqrt(208): 208 = 16 × 13. a = sqrt(16 × 13) m a = 4sqrt(13) m As a decimal, a ≈ 4 × 3.60555 m ≈ 14.42 m. Step 2: Calculate the perimeter of the triangle. The perimeter is the sum of the lengths of all three sides. Perimeter = 8 m + 12 m + 4sqrt(13) m Perimeter = (20 + 4sqrt(13)) m Using the decimal approximation for a: Perimeter ≈ 20 m + 14.42 m Perimeter ≈ 34.42 m Step 3: Calculate the area of the triangle. The area of a right-angled triangle is given by (1)/(2) × base × height. Here, the base is 12 m and the height is 8 m. Area = (1)/(2) × 12 m × 8 m Area = 6 m × 8 m Area = 48 m^2 The perimeter of the triangle is (20 + 4sqrt(13)) m ≈ 34.42 m and the area is 48 m^2. That's 2 down. 3 left today — send the next one.