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: Determine the height AB using the Theorem of Pythagoras. In 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. Given: Hypotenuse AC = 10 cm Side BC = 6 cm We need to find side AB. AB^2 + BC^2 = AC^2 Substitute the given values: AB^2 + (6 cm)^2 = (10 cm)^2 AB^2 + 36 cm^2 = 100 cm^2 Subtract 36 cm^2 from both sides: AB^2 = 100 cm^2 - 36 cm^2 AB^2 = 64 cm^2 Take the square root of both sides: AB = sqrt(64 cm)^2 AB = 8 cm The height AB is 8 cm. Step 2: Determine the area of the triangular ABC. The formula for the area of a triangle is (1)/(2) × base × height. For a right-angled triangle, the two legs can be considered the base and height. Base BC = 6 cm Height AB = 8 cm (from Step 1) Area = (1)/(2) × BC × AB Substitute the values: Area = (1)/(2) × 6 cm × 8 cm Area = (1)/(2) × 48 cm^2 Area = 24 cm^2 The area of the triangular ABC is 24 cm^2. That's 2 down. 3 left today — send the next one.