Alice is designing a rectangular garden with a fixed perimeter of 80 meters. If the length of the garden is three times the width, what is the area of the garden in square meters?
["Alice’s Rectangular Garden: Calculating Area with Fixed Perimeter and Proportional Dimensions", "Designing a beautiful garden starts with smart planning—and for Alice, this means working within precise mathematical boundaries. With a fixed perimeter of 80 meters and a length that’s three times the width, Alice is optimizing space while creating a beautifully proportioned rectangular garden. But how big will her garden be? Let’s explore the calculations behind the area.", "### Understanding the Problem", "Alice wants to build a rectangular garden with:", "- A perimeter (P) of 80 meters\n- Length (L) three times the width (W)\n- Area = Length × Width (A = L × W)", "This setup allows her to use algebra to determine dimensions quickly and accurately.", "### Step 1: Use Perimeter Formula", "The perimeter of a rectangle is given by:\n[ P = 2(L + W) ]", "Substituting the known perimeter:\n[ 80 = 2(L + W) ]", "Divide both sides by 2:\n[ 40 = L + W ]", "### Step 2: Apply the Length-to-Width Relationship", "Given that ( L = 3W ), substitute this into the sum equation:\n[ 40 = 3W + W ]\n[ 40 = 4W ]", "Solve for W:\n[ W = \frac{40}{4} = 10 \ ext{ meters} ]", "### Step 3: Find the Length", "Now calculate the length:\n[ L = 3W = 3 \ imes 10 = 30 \ ext{ meters} ]", "### Step 4: Calculate the Area", "Area of a rectangle is:\n[ A = L \ imes W ]\n[ A = 30 \ imes 10 = 300 \ ext{ square meters} ]", "### Final Result", "Alice’s rectangular garden spans 300 square meters, perfectly utilizing the calculated dimensions of 30 meters in length and 10 meters in width—efficiently combining a triple-length-to-width ratio with a realistic 80-meter perimeter.", "This thoughtful design ensures not only optimal space use but also a tidy, scalable layout ideal for gardening, layout planning, or future expansions. By applying basic geometry, Alice turns a simple perimeter constraint into a functional and pleasing outdoor space.", "---", "Keywords: garden area calculation, rectangular garden perimeter, length to width ratio, optimize garden space, perimeter and area formula, Alice garden design", "Meta Description: Discover how Alice designs a 300 m² rectangular garden using a fixed 80-meter perimeter and a 3:1 length-to-width ratio—perfect for efficient outdoor planning."]
