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: Identify the properties of ABC. Given that ABC = 90^, ABC is a right-angled triangle. The lengths of the two shorter sides are AB = 4 cm and BC = 3 cm. Step 2: Calculate the length of the hypotenuse AC using the Pythagorean theorem. In ABC: AC^2 = AB^2 + BC^2 AC^2 = (4\, cm)^2 + (3\, cm)^2 AC^2 = 16\, cm^2 + 9\, cm^2 AC^2 = 25\, cm^2 AC = sqrt(25\, cm)^2 AC = 5\, cm Step 3: Calculate the area of ABC. The area of a right-angled triangle can be calculated as half the product of its perpendicular sides. Area = (1)/(2) × base × height Using AB and BC as base and height: Area = (1)/(2) × BC × AB Area = (1)/(2) × 3\, cm × 4\, cm Area = (1)/(2) × 12\, cm^2 Area = 6\, cm^2 Step 4: Use the area of ABC to find the length of BD. Given that BDC = 90^, BD is the altitude from B to the hypotenuse AC. We can also express the area of ABC using AC as the base and BD as the height: Area = (1)/(2) × AC × BD We know the Area is 6\, cm^2 and AC = 5\, cm. 6\, cm^2 = (1)/(2) × 5\, cm × BD Multiply both sides by 2: 12\, cm^2 = 5\, cm × BD Divide by 5\, cm: BD = 12\, cm^25\, cm BD = 2.4\, cm The length of BD is 2.4 cm. Send me the next one 📸