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 given information for the first triangle. The base of the first triangle is b_1 = 14 cm. The area of the first triangle is A_1 = 98 cm^2. Step 2: Calculate the area of the second triangle. The problem states that the area of the second triangle (A_2) is double the area of the first triangle (A_1). A_2 = 2 × A_1 A_2 = 2 × 98 cm^2 A_2 = 196 cm^2 Step 3: Identify the given information for the second triangle. The base of the second triangle is b_2 = 14 cm (same as the first triangle). The area of the second triangle is A_2 = 196 cm^2. We need to find the height of the second triangle, h_2. Step 4: Use the formula for the area of a triangle to find the height of the second triangle. The formula for the area of a triangle is: A = (1)/(2) × base × height For the second triangle: A_2 = (1)/(2) × b_2 × h_2 Substitute the known values: 196 cm^2 = (1)/(2) × 14 cm × h_2 196 cm^2 = 7 cm × h_2 Now, solve for h_2: h_2 = 196 cm^27 cm h_2 = 28 cm The height of the second triangle is 28 cm. Comparing this with the given options: A. 21 cm B. 7 cm C. 28 cm D. 14 cm The correct option is C. The final answer is 28 cm.