A rectangle has a length that is 3 times its width. If the perimeter is 48 meters, what are the dimensions of the rectangle?
["1. Intro: Curiosity Drives Discovery \nWhy does a simple rectangle — where length is three times the width — matter beyond geometry class? Today, questions like this are gaining steady traction, especially in niche community groups, home improvement forums, and design-focused content. The shape’s predictable ratio and practical applications spark interest beyond textbooks, especially as users explore space planning, architecture, and visual design trends. With a perimeter of 48 meters, solving for its true dimensions is more than a math problem—it’s a gateway to understanding how proportions shape real-world space.", "2. Why This Rectangular Shape Is Gaining Attention \nThe idea that “length is three times width” isn’t just abstract theory. It reflects balanced proportions used in design, construction, and even everyday decision-making. In the US, interest in optimizing physical spaces — from small urban apartments to professional work environments — fuels demand for precise measurements and smart space solutions. This formula often emerges when planning rectangular rooms, shelves, or even outdoor layouts where symmetry and efficiency are key. The growing popularity of DIY home projects further amplifies practical problems like these, making geometry unairable for users seeking clear answers.", "3. The Math Behind the Rectangle: Step-by-Step Explanation \nLet’s break it down clearly. A rectangle has two pairs of equal opposite sides. If the width is \( w \), then the length is \( 3w \). The perimeter \( P \) of any rectangle is calculated as: \n\[\nP = 2 \ imes (\ ext{length} + \ ext{width}) \n\] \nSubstitute values: \n\[\n48 = 2 \ imes (3w + w) \n\] \nSimplify: \n\[\n48 = 2 \ imes 4w = 8w \n\] \nThen solve: \n\[\nw = 6 \n\] \nNow calculate length: \n\[\n\ ext{length} = 3w = 18 \n\] \nThe rectangle measures 18 meters in length and 6 meters in width — a ratio that balances space use and visual harmony.", "4. Common Questions About This Rectangle Problem \n- Does this mean every 1:3-length rectangle with 48m perimeter follows this? \n Not exactly — this only applies when length is precisely 3 times width. \n- Can this shape apply to real-world rooms? \n Yes, especially in planning furniture layouts or renovation projects. \n- What if the perimeter changes? \n Adjust the width and recalculate using \( 48 = 8w \); every increase in width shifts both sides proportionally. \n- Are there other valid rectangles with perimeter 48m? \n While squares and near-square shapes are common, only the 3:1 ratio gives exact dimensions that satisfy the constraint.", "**5"]
