A rectangular field has a length that is three times its width. If the perimeter of the field is 160 meters, what are the dimensions of the field?
["Rectangular Field Dimensions: Finding Length and Width Given Perimeter and Ratio", "If you're tasked with determining the dimensions of a rectangular field where the length is three times its width and the total perimeter is 160 meters, solving this common geometry problem is straightforward—once you understand the relationship between length, width, and perimeter.", "### Understanding the Problem", "We know from geometry that:", "- The perimeter (P) of a rectangle is calculated by the formula:\n [\n P = 2 \ imes (\ ext{length} + \ ext{width})\n ]", "- In this scenario, the length is three times the width. Let’s represent the width as ( w ). Then the length is ( 3w ).", "### Setting Up the Equation", "Substitute the expressions for length and width into the perimeter formula:", "[\n160 = 2 \ imes (3w + w)\n]", "Simplify inside the parentheses:", "[\n160 = 2 \ imes 4w\n]", "[\n160 = 8w\n]", "Now, solve for ( w ):", "[\nw = \frac{160}{8} = 20 \ ext{ meters}\n]", "### Finding the Length", "Since the length is three times the width:", "[\n\ ext{length} = 3w = 3 \ imes 20 = 60 \ ext{ meters}\n]", "### Final Dimensions", "- Width: 20 meters\n- Length: 60 meters", "This rectangular field measures 20 meters wide by 60 meters long, perfectly matching the given perimeter of 160 meters.", "### Why This Matters", "Knowing how to calculate dimensions from perimeter and ratios is valuable in fields like agriculture, construction, and urban planning. Whether you’re designing a farmland plot or planning a building site, understanding these basics ensures accuracy and efficiency.", "---", "Summary:\nFor a rectangle with length equal to three times the width and a perimeter of 160 meters, the field measures 20 meters by 60 meters. Use the formula ( P = 2(l + w) ) and apply the ratio to solve for both dimensions efficiently.", "### Keywords:\nrectangular field dimensions, perimeter formula, length and width calculation, geometry problem solution, field measurement, algebra applied geometry"]
