A rectangle's length is increased by 20% and its width is decreased by 10%. If the original dimensions are 50 cm by 30 cm, calculate the new area of the rectangle.

["How a 20% Increase in Length and 10% Decrease in Width Affects the Area of a Rectangle: A Practical Example", "When designing products, calculating material needs, or optimizing space, understanding how changes in dimensions affect area is essential. In this article, we explore a common geometric transformation—modifying a rectangle’s length and width—and demonstrate how a 20% increase in length paired with a 10% decrease in width impacts the resulting area. We use a real-world example: a rectangle with original dimensions of 50 cm by 30 cm, and compute the new area after the adjustments.", "### Original Dimensions and Area", "The rectangle starts with:\n- Length = 50 cm\n- Width = 30 cm", "The original area is calculated as:\n[\n\ ext{Area}{\ ext{original}} = \ ext{Length} \ imes \ ext{Width} = 50 \ imes 30 = 1,500 \ ext{ cm}^2\n]", "### New Dimensions After Adjustments", "The rectangle undergoes two key changes:\n- Length is increased by 20%\n- Width is reduced by 10%", "We calculate each new dimension using percentage changes:", "New Length:\n20% increase means the new length is 120% of the original:\n[\n\ ext{New Length} = 50 \ imes (1 + 0.20) = 50 \ imes 1.20 = 60 \ ext{ cm}\n]", "New Width:\n10% decrease means the new width is 90% of the original:\n[\n\ ext{New Width} = 30 \ imes (1 - 0.10) = 30 \ imes 0.90 = 27 \ ext{ cm}\n]", "### New Area Calculation", "With the updated dimensions, the new area is:\n[\n\ ext{Area}^2}} = \ ext{New Length} \ imes \ ext{New Width} = 60 \ imes 27 = 1,620 \ ext{ cm\n]", "### Comparison and Insight", "- Original area: 1,500 cm²\n- New area: 1,620 cm²\n- Increase in area: ( 1,620 - 1,500 = 120 \ ext{ cm}^2 )\n- Percentage increase:\n[\n\frac{120}{1500} \ imes 100% = 8%\n]", "Although width shrank by 10% and length increased by 20%, the net result is a positive 8% increase in area. This occurs because the 20% growth in length has a greater relative impact than the 10% shrink in width—highlighting how proportional changes interact in area calculations.", "### Why This Matters", "Understanding area changes due to dimensional adjustments is key across many fields—architecture, fashion design, manufacturing, and digital graphics. Even small percentage shifts in dimensions can significantly affect usable space, material costs, or visual ratios, making precise calculation vital for accuracy and efficiency.", "---", "Summary:\nOriginal: 50 cm × 30 cm → 1,500 cm²\nAfter 20% length increase and 10% width decrease: 60 cm × 27 cm → 1,620 cm² new area, reflecting an 8% overall increase. This transformation illustrates how strategic dimension changes can enhance or optimize geometric properties.", "Keywords: rectangle area calculation, 20% length increase rectangle, 10% width decrease area, geometric shape changes, area optimization, percentage change in dimensions, rectangle modifications."]