A rectangular garden has a length that is three times its width. If the garden’s area is 192 square meters, what is the garden’s width?
["How to Find the Width of a Rectangular Garden When Length Is Three Times the Width and Area Is 192 Square Meters", "When designing a garden, one of the most practical math problems involves calculating dimensions based on area and the relationship between length and width. In this article, we explore a classic rectangular garden problem: determining the width when the length is three times the width, and the total area is 192 square meters.", "---", "### Understanding the Problem", "You’re given two key facts:\n- The length (L) of the garden is three times the width (W) → $ L = 3W $\n- The area (A) of the garden is 192 square meters → $ A = 192 , \ ext{m}^2 $", "Since the garden is rectangular, the area is calculated by multiplying length and width:\n$$\nA = L \ imes W\n$$", "Substitute $ L = 3W $ into the area formula:\n$$\n192 = 3W \ imes W = 3W^2\n$$", "---", "### Solving for the Width", "Start with the equation:\n$$\n3W^2 = 192\n$$", "Divide both sides by 3:\n$$\nW^2 = \frac{192}{3} = 64\n$$", "Take the square root of both sides:\n$$\nW = \sqrt{64} = 8\n$$", "---", "### Final Answer", "The width of the garden is 8 meters.\nSince the length is three times the width, the length is:\n$$\nL = 3 \ imes 8 = 24 , \ ext{meters}\n$$", "Verifying:\n$$\n\ ext{Area} = 8 \ imes 24 = 192 , \ ext{m}^2 \quad \ ext{✓}\n$$", "---", "### Why This Calculation Matters", "Understanding how to set up and solve equations based on real-world shapes like rectangular gardens helps homeowners, landscapers, and gardening enthusiasts plan space efficiently. Knowing the width enables better decisions about planting, fencing, irrigation, and design placement.", "---", "Summary:\nGiven a rectangular garden where the length is three times the width and the area is 192 square meters, the width is 8 meters. Use $ L = 3W $ and $ A = L \ imes W $ to derive solutions for common garden dimensions effortlessly.", "---", "Keywords: rectangular garden, garden width, area calculation, length three times width, solve garden dimensions, rectangle area problem, real-world math, garden planning, math in gardening", "Meta Description: Learn how to find the width of a rectangular garden where the length is three times the width and the area is 192 square meters using algebra. Step-by-step solution."]
