A rectangle has a length that is 4 times its width. If its perimeter is 90 meters, what is its area?
["Rectangle Perimeter and Area: Solve Using Given Ratio and Measure", "Understanding geometry is essential when tackling real-world problems involving areas and perimeters. One classic example is determining a rectangle’s dimensions, area, and other properties based on proportional relationships. In this article, we’ll explore a scenario where a rectangle’s length is four times its width, and its perimeter is 90 meters—then calculate the area using step-by-step math.", "### Setting Up the Problem", "We know:\n- The rectangle’s length ((L)) is 4 times its width ((W)).\n- The perimeter ((P)) of the rectangle is 90 meters.", "From geometry, the formula for the perimeter of a rectangle is:", "[\nP = 2L + 2W\n]", "Since (L = 4W), we substitute this into the perimeter equation:", "[\n90 = 2(4W) + 2W\n]", "Simplify the equation:", "[\n90 = 8W + 2W = 10W\n]", "Solve for (W):", "[\nW = \frac{90}{10} = 9 \ ext{ meters}\n]", "### Find the Length", "Now that we know the width, we find the length:", "[\nL = 4W = 4 \ imes 9 = 36 \ ext{ meters}\n]", "### Calculate the Area", "The area ((A)) of a rectangle is given by:", "[\nA = L \ imes W = 36 \ imes 9\n]", "Multiply to find the area:", "[\nA = 324 \ ext{ square meters}\n]", "---", "### Summary", "- Width: 9 meters\n- Length: 36 meters\n- Perimeter: 90 meters (as given)\n- Area: 324 m²", "This problem shows how proportional relationships and algebraic substitution simplify geometric calculations. Whether for construction, design, or everyday math practice, mastering these steps enhances your ability to solve similar real-life geometry challenges.", "---", "Keywords: rectangle area formula, perimeter calculation, geometry problem solving, length multiplied by width, solving for unknowns in rectangles, 4 times width rectangle, perimeter 90 m, math tutorial", "Meta Description: Solve for a rectangle’s area when length is 4 times its width and the perimeter is 90 meters. Step-by-step example with calculations."]
