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
The image shows an isosceles triangle ABC with AB = AC = 8 and an altitude AD = 4. We need to find the length of the base BC. Step 1: Identify the properties of the triangle. Since ABC is an isosceles triangle with AB = AC, the altitude AD to the base BC also bisects the base. This means BD = DC. Also, AD is perpendicular to BC, forming two right-angled triangles, ADB and ADC. Step 2: Use the Pythagorean theorem in ADC. In the right-angled triangle ADC, we have the hypotenuse AC = 8 and one leg AD = 4. We can find the length of the other leg DC using the Pythagorean theorem: AD^2 + DC^2 = AC^2. 4^2 + DC^2 = 8^2 16 + DC^2 = 64 DC^2 = 64 - 16 DC^2 = 48 Step 3: Calculate the length of DC. Take the square root of both sides to find DC: DC = sqrt(48) To simplify the radical, find the largest perfect square factor of 48, which is 16: DC = sqrt(16 × 3) DC = 4sqrt(3) Step 4: Calculate the length of BC. Since AD bisects BC, BC = 2 × DC. BC = 2 × 4sqrt(3) BC = 8sqrt(3) The length of BC is 8sqrt(3). Send me the next one 📸