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

["Title: How Increasing Length by 20% and Decreasing Width by 10% Changes a Rectangle’s Area – A Step-by-Step Calculation", "When designing products, architectural plans, or even garden layouts, understanding how changes in dimensions affect area is essential. One common scenario involves altering a rectangle’s length and width, which directly impacts its usable space. In this article, we explore how increasing a rectangle’s length by 20% and decreasing its width by 10% affects the overall area—using precise calculations based on original dimensions of 50 cm by 30 cm.", "### Original Dimensions\nStart with the original measurements:\n- Length = 50 cm\n- Width = 30 cm", "The original area is calculated as:\n[ \ ext{Area} = \ ext{Length} \ imes \ ext{Width} = 50 , \ ext{cm} \ imes 30 , \ ext{cm} = 1,500 , \ ext{cm}^2 ]", "### Adjusting Dimensions\nThe problem specifies two percentage-based changes:\n- The length is increased by 20%\n- The width is decreased by 10%", "Let’s compute the new dimensions step by step.", "1. New Length:\nA 20% increase on 50 cm means adding 20% of 50 to the original length:\n[ \ ext{New length} = 50 + (0.20 \ imes 50) = 50 + 10 = 60 , \ ext{cm} ]", "2. New Width:\nA 10% decrease on 30 cm means subtracting 10% of 30 from the original width:\n[ \ ext{New width} = 30 - (0.10 \ imes 30) = 30 - 3 = 27 , \ ext{cm} ]", "### Calculating the New Area\nNow multiply the updated length and width to find the new area:\n[ \ ext{New area} = 60 , \ ext{cm} \ imes 27 , \ ext{cm} = 1,620 , \ ext{cm}^2 ]", "### Percentage Change in Area\nTo fully understand the impact, let’s compute the area change:\nOriginal area: 1,500 cm²\nNew area: 1,620 cm²\nIncrease = ( 1,620 - 1,500 = 120 , \ ext{cm}^2 )\nPercentage increase =\n[ \left( \frac{120}{1,500} \right) \ imes 100 = 8% ]", "Although width decreased, the longer length had a stronger effect, resulting in an overall 8% increase in area despite the reduction in width.", "### Conclusion\nBy increasing a rectangle’s length by 20% and decreasing its width by 10%, the new area becomes 1,620 cm², showing how strategic dimensional shifts can significantly reshape usable space. This insight helps in optimizing space in design and engineering projects.", "If you're planning design changes or spatial adjustments, remember: small percentage shifts can lead to meaningful gains—or losses—in total area. Always calculate the new dimensions before finalizing your measurements.", "---", "Keywords: rectangle area calculation, length increase 20%, width decrease 10%, area change formula, rectangular dimensions change, 50 cm × 30 cm rectangle, mathematical area computation, geometry optimization."]