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.
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Based on the image, it appears to be a right-angled triangle ABC, with the right angle at B. The given side lengths are AB = 12 cm and BC = 5 cm. You need to calculate the length of AC, the area, and the perimeter of the triangle. a) Calculate AC Step 1: Use the Pythagorean theorem, which states that for a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (a^2 + b^2 = c^2). AC^2 = AB^2 + BC^2 Step 2: Substitute the given values into the formula. AC^2 = (12 cm)^2 + (5 cm)^2 AC^2 = 144 cm^2 + 25 cm^2 Step 3: Add the values and find the square root to get the length of AC. AC^2 = 169 cm^2 AC = sqrt(169 cm)^2 AC = 13 cm b) Calculate the area of triangle ABC Step 1: The area of a right-angled triangle is given by the formula (1)/(2) × base × height. In this case, AB and BC are the base and height. Area = (1)/(2) × AB × BC Step 2: Substitute the known values into the formula. Area = (1)/(2) × 12 cm × 5 cm Step 3: Perform the multiplication to find the area. Area = (1)/(2) × 60 cm^2 Area = 30 cm^2 c) Calculate the perimeter of triangle ABC Step 1: The perimeter of a triangle is the sum of the lengths of all its sides. Perimeter = AB + BC + AC Step 2: Substitute the lengths of the sides (including AC calculated in part a) into the formula. Perimeter = 12 cm + 5 cm + 13 cm Step 3: Add the lengths to find the total perimeter. Perimeter = 30 cm Send me the next one 📸