A rectangle has a perimeter of 40 cm and a length that is 3 times its width. Find its area.
["Rectangle with Perimeter 40 cm and Length 3 Times Width: Find the Area", "If you’re working on geometry problems, understanding how to calculate the area of a rectangle using given constraints—like a fixed perimeter and a relationship between length and width—is essential. In this article, we’ll solve a classic problem: finding the area of a rectangle with a perimeter of 40 cm and a length that is three times its width.", "---", "### Problem Setup", "We are given:", "- Perimeter of the rectangle = 40 cm\n- Length ( l ) = 3 × width ( w )", "We need to find the area of the rectangle.", "---", "### Step 1: Recall the perimeter formula", "The perimeter ( P ) of a rectangle is:", "[\nP = 2(l + w)\n]", "Substitute the given perimeter:", "[\n40 = 2(l + w)\n]", "Divide both sides by 2:", "[\nl + w = 20\n]", "---", "### Step 2: Use the relationship between length and width", "Given ( l = 3w ), substitute into the equation above:", "[\n3w + w = 20\n]", "[\n4w = 20\n]", "Solve for ( w ):", "[\nw = \frac{20}{4} = 5 \ ext{ cm}\n]", "---", "### Step 3: Find the length", "Now use ( l = 3w ):", "[\nl = 3 \ imes 5 = 15 \ ext{ cm}\n]", "---", "### Step 4: Calculate the area", "The area ( A ) of a rectangle is:", "[\nA = l \ imes w = 15 \ imes 5 = 75 \ ext{ cm}^2\n]", "---", "### Summary", "- Width = 5 cm\n- Length = 15 cm\n- Perimeter = 40 cm (confirmed: ( 2(15 + 5) = 40 ))\n- Area = 75 cm², verified by calculation", "---", "### Why This Problem Matters", "Understanding how to tie perimeter constraints to shape dimensions helps solve practical problems in architecture, carpentry, and design. Knowing that a rectangle with a 40 cm perimeter and length 3× its width clearly has an area of 75 cm² is foundational for geometry and real-world measurements.", "---", "Key Takeaway:\nGiven perimeter and ratio of sides, algebra—especially substitution—lets you solve for length, width, and ultimately area without errors.", "---", "Keywords for SEO:\nrectangle perimeter 40 cm, rectangle length 3× width, find area of rectangle, solve geometry problem, rectangle area formula, perimeter and dimensions, geometry step-by-step, solve algebra geometry problem."]
