A rectangle has a perimeter of 60 cm. If the length is 3 times the width, what is the area of the rectangle?
["A Rectangle with a Perimeter of 60 cm: How to Find the Area When Length Equals 3 Times the Width", "Understanding the relationship between a rectangle’s perimeter, length, and width is key to solving geometry problems efficiently. In this article, we explore a classic geometry question: A rectangle has a perimeter of 60 cm. If the length is 3 times the width, what is the area of the rectangle? Let’s break it down step by step.", "---", "### Understanding the Problem", "We’re given:", "- The perimeter of the rectangle is 60 cm\n- The length (L) is 3 times the width (W)\n- We need to find the area of the rectangle", "This type of problem combines algebraic equations with geometric formulas, making it accessible for students and math enthusiasts alike.", "---", "### Step 1: Recall the Perimeter Formula", "The perimeter (P) of a rectangle is calculated using:", "[\nP = 2 \ imes (\ ext{Length} + \ ext{Width}) = 2(L + W)\n]", "Given that ( P = 60 ), we substitute:", "[\n2(L + W) = 60\n]", "Divide both sides by 2:", "[\nL + W = 30 \ ag{1}\n]", "---", "### Step 2: Use the Relationship Between Length and Width", "We’re told the length is 3 times the width:", "[\nL = 3W \ ag{2}\n]", "---", "### Step 3: Substitute and Solve for Width", "Plug Equation (2) into Equation (1):", "[\n3W + W = 30\n]", "[\n4W = 30\n]", "[\nW = \frac{30}{4} = 7.5\ \ ext{cm}\n]", "---", "### Step 4: Find the Length", "Now substitute ( W = 7.5 ) back into ( L = 3W ):", "[\nL = 3 \ imes 7.5 = 22.5\ \ ext{cm}\n]", "---", "### Step 5: Calculate the Area", "The area (A) of a rectangle is:", "[\nA = \ ext{Length} \ imes \ ext{Width}\n]", "[\nA = L \ imes W = 22.5 \ imes 7.5 = 168.75\ \ ext{cm}^2\n]", "---", "### Final Answer", "[\n\boxed{168.75\ \ ext{cm}^2}\n]", "---", "### Why This Problem Matters", "This example illustrates how combining algebraic equations with a geometric formula enables clear, step-by-step problem solving. Knowing how to express relationships between dimensions helps in real-world applications like construction, design, and space planning.", "If you're studying geometry or preparing for exams, practice problems like this help master core concepts reliably. Try finding other rectangle problems—changing perimeter or length-to-width ratios—to strengthen your skills!", "---", "Keywords: rectangle perimeter, area calculation, length and width relationship, 3 times width, geometry problem solution, solving for dimensions, rectangle area formula, 60 cm perimeter, math tutorial", "Meta Description: Solve a common geometry problem: a rectangle with a 60 cm perimeter and length 3 times the width. Learn step-by-step how to calculate its area of 168.75 cm²."]
