A rectangular prism has volume 120 cubic inches. Its length is twice its width, and its height is 5 inches. What is the width?
["Title: Solve for the Width of a Rectangular Prism with Given Dimensions and Volume", "Calculating the volume of a rectangular prism is a common math problem in geometry, and when real-world constraints are included—like relationships between dimensions—it becomes both practical and engaging. In this article, we’ll explore a classic volume calculation with a twist: finding the width of a rectangular prism given its volume, a proportion between its dimensions, and a fixed height.", "### The Problem: Given Volume and Dimension Relationships", "We are given that a rectangular prism has a volume of 120 cubic inches.\nThe length is twice the width, and the height is 5 inches.\nWe are asked to find the width of the prism.", "---", "### Step 1: Use the Volume Formula for a Rectangular Prism", "The volume ( V ) of a rectangular prism is calculated using the formula:", "[\nV = \ ext{length} \ imes \ ext{width} \ imes \ ext{height}\n]", "We are given:\n- ( V = 120 ) cubic inches\n- ( \ ext{height} = 5 ) inches\n- ( \ ext{length} = 2 \ imes \ ext{width} )", "Let the width be ( w ). Then the length is ( 2w ).", "Substitute into the volume formula:", "[\n120 = (2w) \ imes w \ imes 5\n]", "---", "### Step 2: Simplify and Solve for ( w )", "[\n120 = 2w \cdot w \cdot 5\n]\n[\n120 = 10w^2\n]", "Divide both sides by 10:", "[\nw^2 = 12\n]", "Take the square root:", "[\nw = \sqrt{12} = 2\sqrt{3} \ ext{ inches}\n]", "---", "### Step 3: Final Answer", "The width of the rectangular prism is ( 2\sqrt{3} ) inches, which is approximately 3.464 inches.", "---", "### Why This Problem Matters", "This type of problem teaches key concepts in algebra and geometry:\n- Understanding volume formulas\n- Translating proportional relationships into equations\n- Using square roots to solve quadratic equations", "It’s a great exercise for students, teachers, and anyone looking to sharpen problem-solving skills in mathematics.", "---", "Ready to calculate your own rectangular prism? Whether for a classroom assignment, DIY project, or just casual learning, mastering these steps will help you tackle similar real-world geometry challenges with confidence.", "Keywords: rectangular prism volume, rectangular prism dimensions, solve for width, geometry problem with proportions, volume formula, square root calculation, math problem solving."]
