A rectangular garden has a length 3 times its width. If the perimeter is 160 meters, what is the area in square meters?
["Rectangular Garden: Understanding Dimensions, Perimeter, and Area with a 160-Meter Perimeter", "If you’re designing a rectangular garden and know that the length is three times the width, understanding how to calculate both the dimensions and area can help you maximize space efficiently. In this article, we explore a classic garden example: a rectangular plot where the length is three times the width and the total perimeter is 160 meters. We’ll break down the math step-by-step to find the exact area — a key factor in garden planning.", "---", "### Given Information", "- The garden is rectangular.\n- Length (L) = 3 × Width (W)\n- Perimeter (P) = 160 meters\n- We are to find the Area in square meters", "---", "### Step 1: Use the Perimeter Formula for a Rectangle", "The perimeter of a rectangle is calculated with the formula:", "[\nP = 2 \ imes (L + W)\n]", "Substitute the known values:\n160 = 2 × (L + W)", "Divide both sides by 2:", "[\nL + W = 80\n]", "---", "### Step 2: Substitute Length in Terms of Width", "Since L = 3W, replace L in the equation:", "[\n3W + W = 80\n]", "[\n4W = 80\n]", "Solve for W:", "[\nW = 20 \ ext{ meters}\n]", "Now calculate the length:", "[\nL = 3 \ imes 20 = 60 \ ext{ meters}\n]", "---", "### Step 3: Calculate the Area", "Area of a rectangle is:", "[\nA = L \ imes W = 60 \ imes 20 = 1200 \ ext{ square meters}\n]", "---", "### Conclusion", "A rectangular garden with a length three times its width and a perimeter of 160 meters has an area of 1,200 square meters. This ample space is ideal for growing a variety of plants, arranging garden beds, or adding paths — all while leveraging precise mathematical relationships for efficient design.", "---", "Keywords: rectangular garden perimeter, garden area calculation, length three times width, rectangular garden math, how to find garden area, perimeter and area problems, garden design math", "---", "Meta Description:\nDiscover how to calculate the area of a rectangular garden where the length is three times the width and the perimeter is 160 meters. Learn step-by-step math to optimize your garden space efficiently.", "---", "Efficient garden planning begins with clear calculations — start today with this simple but powerful formula!"]
