A rectangular garden has a length that is 4 times its width. If the perimeter of the garden is 90 meters, what is the area of the garden?
["How to Calculate the Area of a Rectangular Garden Given Its Perimeter and Dimensions", "When designing a garden, understanding its dimensions is key to maximizing both aesthetics and usability. One classic problem involves a rectangular garden where the length is four times the width, and knowing the perimeter helps determine the exact area—a critical factor for planning plants, pathways, and garden beds.", "This article breaks down how to find the area of a rectangular garden when its perimeter is 90 meters and its length is four times its width.", "---", "### Understanding the Problem", "We are told:", "- The garden is rectangular.\n- The length (L) is 4 times the width (W) → ( L = 4W )\n- The perimeter is 90 meters: ( P = 90 , \ ext{m} )\n- We need to find the area: ( A = L \ imes W )", "---", "### Step 1: Use the Perimeter Formula", "The perimeter ( P ) of a rectangle is given by:\n[\nP = 2(L + W)\n]", "Substitute ( L = 4W ) into the formula:", "[\n90 = 2(4W + W)\n]\n[\n90 = 2(5W)\n]\n[\n90 = 10W\n]", "---", "### Step 2: Solve for Width (W)", "[\nW = \frac{90}{10} = 9 , \ ext{meters}\n]", "---", "### Step 3: Find the Length (L)", "[\nL = 4W = 4 \ imes 9 = 36 , \ ext{meters}\n]", "---", "### Step 4: Calculate the Area", "[\nA = L \ imes W = 36 \ imes 9 = 324 , \ ext{square meters}\n]", "---", "### Why Knowing the Perimeter Matters", "A well-defined perimeter allows gardeners to:", "- Plan efficient watering and irrigation systems\n- Choose appropriate garden bed sizes and plant spacing\n- Estimate materials needed for fencing or mulch", "Combining this with the known ratio between length and width gives precise spatial insights—like this garden’s 324 m² area.", "---", "### Summary", "| Dimension | Value |\n|-----------|----------|\n| Width (W) | 9 meters |\n| Length (L)| 36 meters|\n| Perimeter | 90 meters |\n| Area | 324 m² |", "When the length is four times the width and the perimeter is 90 meters, the garden measures 9 meters in width and 36 meters in length, yielding a spacious 324 square meters of usable outdoor space.", "---", "Optimize your garden planning by using simple geometry—know your perimeter, define your dimensions, and calculate your area with confidence!"]
