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 relevant triangle and given lengths. The problem asks for the length of BC. From the diagram, ABC is a right-angled triangle with the right angle at B. The given lengths are AB = 7 cm. The diagram indicates AC = 20 cm. (Note: The text states AD = 12 cm, but this length is not directly used for finding BC in ABC. We will use AC = 20 cm as shown in the diagram for ABC.) Step 2: Apply the Pythagorean theorem. For a right-angled triangle, the Pythagorean theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In ABC: AB^2 + BC^2 = AC^2 Step 3: Substitute the known values into the equation. Substitute AB = 7 cm and AC = 20 cm: 7^2 + BC^2 = 20^2 49 + BC^2 = 400 Step 4: Solve for BC. Subtract 49 from both sides: BC^2 = 400 - 49 BC^2 = 351 Take the square root of both sides: BC = sqrt(351) Calculating the numerical value and rounding to two decimal places: BC ≈ 18.73 cm The length of BC is 18.73 cm. Send me the next one 📸