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: Write the formula for the volume of a triangular prism. The volume V of a triangular prism is given by the formula: V = (1)/(2) × base of triangle × height of triangle × length of prism Using the variables from the diagram: V = (1)/(2) × y × 12 cm × 8 cm Step 2: Substitute the given volume into the formula. We are given that the volume V = 800 cm^3. 800 cm^3 = (1)/(2) × y × 12 cm × 8 cm Step 3: Simplify the equation and solve for y. First, multiply the known numerical values: 800 = (1)/(2) × y × (12 × 8) 800 = (1)/(2) × y × 96 Now, multiply (1)/(2) by 96: 800 = 48y To find y, divide both sides by 48: y = (800)/(48) y = 16.666... cm Step 4: Round the answer to one decimal place. Rounding 16.666... to one decimal place gives 16.7. y ≈ 16.7 cm The length base y must be 16.7 cm. Send me the next one 📸