Un terrain rectangulaire a une longueur qui est le double de sa largeur. Si le périmètre du terrain est de 180 mètres, quelle est l'aire du terrain ?
["Title: How to Calculate the Area of a Rectangular Plot with a 2:1 Length-to-Width Ratio and a Perimeter of 180 Meters", "When faced with a practical geometry problem, understanding how shape dimensions relate is key. Today, we explore a common real-world scenario: calculating the area of a rectangular plot where the length is twice the width and the perimeter is 180 meters.", "### Understanding the Problem", "We know two essential facts:\n- The length ((L)) of the rectangular plot is twice its width ((W)):\n [\n L = 2W\n ]\n- The perimeter of the rectangle is 180 meters.\n The general formula for the perimeter (P) of a rectangle is:\n [\n P = 2(L + W)\n ]", "### Step-by-Step Calculation", "1. Substitute the ratio into the perimeter formula.\n Since (L = 2W), plug this into the perimeter equation:\n [\n 180 = 2(2W + W)\n ]\n Simplify inside the parentheses:\n [\n 180 = 2(3W) = 6W\n ]", "2. Solve for the width:\n [\n W = \frac{180}{6} = 30 \ ext{ meters}\n ]", "3. Find the length using the ratio:\n [\n L = 2W = 2 \ imes 30 = 60 \ ext{ meters}\n ]", "4. Calculate the area:\n The area (A) of a rectangle is given by:\n [\n A = L \ imes W = 60 \ imes 30 = 1800 \ ext{ square meters}\n ]", "### Conclusion", "By applying basic geometry principles and algebraic relationships, we determined that a rectangular plot with a length twice its width and a perimeter of 180 meters has a total area of 1,800 m². This method helps quickly solve similar problems in architecture, landscaping, or land planning, ensuring accurate measurements and efficient resource use.", "If you’re tasked with measuring a similar space, remember:\n- Use the length-to-width ratio to simplify equations\n- Apply the perimeter formula carefully\n- Multiply length and width to find the area", "Such calculations are essential in construction, surveying, and design — making geometry not just academic, but genuinely practical."]
