A rectangle has an area of 120 square meters and a perimeter of 46 meters. What are the dimensions of the rectangle?
["A rectangle has an area of 120 square meters and a perimeter of 46 meters. What are the dimensions of the rectangle?", "Curious about geometric puzzles that blend real-world logic with problem-solving? If you’ve stumbled across a rectangle with a fixed area of 120 square meters and a perimeter of 46 meters, you’re not just curious—you’re engaging with a classic math challenge that’s popping up in classrooms, design communities, and online forums across the U.S. Solving for the exact length and width isn’t just academic; it connects to everyday applications in architecture, landscaping, packaging, and more.", "What’s the mystery behind this rectangle? How can both area and perimeter be precisely defined with these two numbers? The answer reveals not just a calculation, but a deeper appreciation for how geometry shapes practical decisions in design and engineering.", "Why this rectangle matters today", "This problem resonates because it reflects a common real-world tension: how to optimize space under physical constraints. The combination of fixed area and perimeter forces a unique trapezoidal shape in possible dimensions—close to what engineers, architects, and fabricators reason through daily. Recent trends in efficient design, minimalistic living spaces, and eco-conscious resource use amplify interest in such puzzles. More than a brain teaser, this rectangle embodies the logic behind smart space planning that’s cost-effective and sustainable.", "How does a rectangle with 120 m² area and 46 m perimeter work?", "To break it down, start with rectangle formulas:", "- Area = length × width → \( L \ imes W = 120 \) \n- Perimeter = 2(length + width) → \( 2(L + W) = 46 \) → \( L + W = 23 \)", "By combining both equations, you form a simple quadratic equation. Since \( W = 23 - L \), substitute into the area equation:", "\( L(23 - L) = 120 \) \n\( 23L - L^2 = 120 \) \nRearranging: \n\( L^2 - 23L + 120 = 0 \)", "This quadratic reveals two real roots—just two valid length and width pairs—showing how math converges precisely under"]
