A rectangular garden has a length that is 3 times its width. If the perimeter of the garden is 64 meters, what is the area of the garden?
["Rectangular Garden: Calculating Area from Dimensions and Perimeter", "When designing a garden, understanding its shape and dimensions is essential to maximizing space and aesthetics. A common and efficient shape is a rectangular garden, where the relationships between length and width often follow precise mathematical rules. Today, we explore a practical example: a rectangular garden where the length is three times the width, and the perimeter is 64 meters. By leveraging these constraints, we’ll calculate not just the perimeter but, more importantly, the area—an essential metric for gardening planning.", "---", "### Understanding the Dimensions", "Let’s define the variables:", "- Let the width of the garden be ( w ) meters.\n- Since the length is 3 times the width, the length ( l = 3w ) meters.", "The perimeter of a rectangle is given by the formula:", "[\nP = 2 \ imes (l + w)\n]", "Given that the perimeter is 64 meters:", "[\n2 \ imes (3w + w) = 64\n]", "Simplify inside the parentheses:", "[\n2 \ imes 4w = 64\n]", "[\n8w = 64\n]", "Now solve for ( w ):", "[\nw = \frac{64}{8} = 8 , \ ext{meters}\n]", "Using this, the length is:", "[\nl = 3 \ imes w = 3 \ imes 8 = 24 , \ ext{meters}\n]", "---", "### Calculating the Area", "The area ( A ) of a rectangle is calculated as:", "[\nA = l \ imes w\n]", "Substitute the known values:", "[\nA = 24 \ imes 8 = 192 , \ ext{square meters}\n]", "---", "### Why This Calculation Matters for Gardeners", "Knowing both perimeter and area is crucial in gardening:", "- Perimeter helps determine the length of edging, fencing, or border material needed.\n- Area tells you how much space you have to plant flowers, vegetables, or lay mulch—directly linking geometry to practical garden design.", "In this example, with a perimeter of 64 meters and dimensions of 24 meters by 8 meters, the garden offers 192 square meters—a substantial space perfect for diverse landscaping or productive gardening.", "---", "### Summary", "- Perimeter = 64 m\n- Width = 8 m\n- Length = 24 m\n- Area = 192 m²", "If you're planning a rectangular garden and know that the length is three times the width, always use the perimeter formula to solve for dimensions, then compute the area to optimize your planting layout and construction resources.", "---", "Keywords: rectangular garden area, perimeter calculation rectangle, length is 3 times width, garden dimensions, calculate garden area, rectangular garden with 64m perimeter, garden layout planning", "Meta Description: Learn how to calculate the area of a rectangular garden when the length is three times the width and the perimeter is 64 meters. Step-by-step guide with perimeter and area formulas."]
