Question:** A rectangular garden is 3 times as long as it is wide. If its perimeter is 64 meters, what is its area?
["Title: Solve This Easy Garden Rectangle Problem: How to Find Area from Perimeter and Ratio", "Meta Description: Struggling to find the area of a rectangular garden with a known perimeter and length-to-width ratio? Learn step-by-step how a 3-to-1 rectangle with a 64-meter perimeter leads to a perfect 288 square meter solution.", "---", "### Unlock the Mystery of Rectangular Gardens: A Perfect Example for DIY Landowners", "Gardening isn’t just about planting flowers and vegetables—it’s also about understanding your space. Many homeowners and garden enthusiasts ask a classic yet practical question: “A rectangular garden is 3 times as long as it is wide. If its perimeter is 64 meters, what is its area?”", "This question seeks more than just a math answer—it’s a gateway to designing efficient, beautiful garden layouts. Let’s break down the problem, solve it step by step, and learn how geometry turns simple measurements into real-world results.", "---", "### Understanding the Problem: Length, Width, and Perimeter", "We’re told:\n- The garden is rectangular\n- The length is 3 times the width\n- The perimeter is 64 meters\n- We need to find the area", "To solve this, we start by recalling the formula for the perimeter of a rectangle:\n[\nP = 2 \ imes (\ ext{length} + \ ext{width})\n]", "Let’s define the variables:\nLet the width be ( w ) meters.\nThen the length is ( 3w ) meters, since it’s 3 times wider.", "---", "### Step 1: Set Up the Perimeter Equation", "Plugging into the perimeter formula:\n[\n64 = 2 \ imes (3w + w)\n]\n[\n64 = 2 \ imes 4w\n]\n[\n64 = 8w\n]\nNow, solve for ( w ):\n[\nw = \frac{64}{8} = 8 \ ext{ meters}\n]", "---", "### Step 2: Find the Length", "Since length = ( 3w ):\n[\n\ ext{length} = 3 \ imes 8 = 24 \ ext{ meters}\n]", "---", "### Step 3: Calculate the Area", "The area ( A ) of a rectangle is:\n[\nA = \ ext{length} \ imes \ ext{width} = 24 \ imes 8\n]\n[\nA = 192 \ ext{ square meters}\n]", "Wait — hold on! Earlier, a common puzzle teaches that with a perimeter of 64 and 3:1 ratio, the area is 288 m², not 192. Where did we go wrong?", "Let’s double-check the perimeter:\nLength = 24, width = 8 → perimeter = ( 2(24 + 8) = 2 \ imes 32 = 64 ) — correct.\nBut wait: The area calculation is solid: 24 × 8 = 192.", "Hmm — contrasting with some famous similar problems?", "---", "### A Well-Known Counterpoint: Why the 288?", "Some variants of this question describe a rectangle with perimeter 64 to equate it to a square’s area — but in standard math problems, a 3:1 rectangle with perimeter 64 yields area 192 m², not 288.", "But let’s explore why 288 appears — and correct the confusion.", "Is 288 the right answer here?\nNo — 192 is.\nBut perhaps the original question implies a different setup, or it’s a common misconception.", "Wait — could the length be 3 times longer than the width, meaning length = width + 3? That’s not the same.", "But when saying “3 times as long as wide,” standard interpretation is:\nlength = 3 × width → correct as 24 and 8.", "So why does 288 show up? Let’s reverse-engineer:", "Suppose identified area was mistakenly 288 — is that possible with different values?", "Try:\n- Let width = ( w ), length = ( 3w )\n- Perimeter = ( 2(w + 3w) = 8w = 64 \Rightarrow w = 8 ), area = 24 × 8 = 192", "192 is correct.\nThe 288 number comes from doubling 144 — possibly from an unrelated problem.", "---", "### Final Correct Solution", "Given:\n- Rectangle with perimeter = 64 m\n- Length = 3 × width", "Let width = ( w ), length = ( 3w )\n[\n2(w + 3w) = 64\n]\n[\n8w = 64 \Rightarrow w = 8\ \ ext{m}\n]\nLength = ( 3 \ imes 8 = 24\ \ ext{m} )\nArea = ( 24 \ imes 8 = 192\ \ ext{m}^2 )", "---", "### Why This Matters for Gardeners", "Understanding how rectangles work allows smarter planning:\n- Efficient use of space for planting rows, walkways, or fencing\n- Accurate material estimates (soil, mulch, fencing)\n- Balanced design that maximizes sunlight and accessibility", "---", "### Pro Tips: Solving Rectangle Area Problems Like This", "1. Restate the ratio clearly: Let width = ( w ), so length = ( 3w )\n2. Use perimeter formula to form an equation\n3. Solve algebraically before multiplying for area\n4. Double-check dimensions to avoid common errors\n5. Visualize — think of tape measures around the garden", "---", "### Final Thoughts", "So, what is the area of a rectangular garden 3 times as long as it is wide, with a perimeter of 64 meters? The answer is 192 square meters — not 288, though 288 remains a memorable number in similar problems. Accurate math leads to better gardens.", "Ready to design your dream space? Measure, calculate, and grow with confidence!", "---", "Keywords: rectangular garden area, calculate rectangular garden area, perimeter and area problem, 3 times width rectangle, 64 meter garden, solve garden math, DIY garden planning", "SEO Meta Tags:\nTitle: How to Find Area of a Rectangle with Perimeter and Ratio\nKeywords: garden perimeter, rectangular area calculation, 3:1 rectangle area, DIY garden math, garden layout guide", "---", "Image suggestion: A diagram of a rectangle with length triple the width, labeled 8m and 24m sides, and area marked 192 m².", "---", "If you’re still asking, “A rectangular garden is 3 times as long as it is wide with a 64-meter perimeter — what’s the area?” now you know the answer is 192 square meters, confirmed by solid geometry and real-world gardening math."]
