A rectangle has a length of 12 cm and a width of 5 cm. If it is scaled up by a factor of 3, what is the area of the new rectangle?
["# Scaling Up a Rectangle: How Area Changes When Dimensions Increase", "When working with geometry, scaling shapes can make a big difference—not just in appearance, but also in measurable properties like area. Take the case of a rectangle with a length of 12 cm and a width of 5 cm. What happens to its area when we scale it up by a factor of 3?", "## Understanding the Original Rectangle", "First, let’s calculate the original area of the rectangle. The formula for the area of a rectangle is:", "[\n\ ext{Area} = \ ext{length} \ imes \ ext{width}\n]", "Substituting the given values:", "[\n\ ext{Original Area} = 12,\ ext{cm} \ imes 5,\ ext{cm} = 60,\ ext{cm}^2\n]", "So, the original rectangle covers 60 square centimeters of space.", "## Scaling Up by a Factor of 3", "Scaling a shape by a factor means multiplying every linear dimension—length and width—by that factor. Here, the scaling factor is 3, so:", "- New length = ( 12,\ ext{cm} \ imes 3 = 36,\ ext{cm} )\n- New width = ( 5,\ ext{cm} \ imes 3 = 15,\ ext{cm} )", "The new rectangle has dimensions 36 cm × 15 cm.", "## Calculating the Area of the Scaled Rectangle", "Now, compute the area of the resized rectangle:", "[\n\ ext{New Area} = 36,\ ext{cm} \ imes 15,\ ext{cm} = 540,\ ext{cm}^2\n]", "Alternatively, you can use the scaling principle in area calculations: when scaling a two-dimensional shape by a factor ( k ), the area scales by ( k^2 ).", "[\n\ ext{New Area} = \ ext{Original Area} \ imes k^2 = 60,\ ext{cm}^2 \ imes 3^2 = 60 \ imes 9 = 540,\ ext{cm}^2\n]", "## Why This Matters", "Understanding how area scales with size is essential in fields like architecture, engineering, graphic design, and manufacturing. Even a small shape like a rectangle can represent significant space when scaled—especially when preparing blueprints or packaging materials.", "---", "In summary: Scaling a rectangle of 12 cm by 5 cm by a factor of 3 increases its area from 60 cm² to 540 cm². This demonstrates the powerful effect of multiplicative scaling on two-dimensional measurements.", "---", "Key takeaways:\n- Original area: 60 cm²\n- Scaled dimensions: 36 cm × 15 cm\n- Scaled area: 540 cm²\n- Area scales by the square of the linear scale factor (3² = 9)", "---", "Start calculating smarter today—know how scaling affects area to avoid errors in design, construction, and everyday problem-solving!"]
