Final Answer:
Carmen's reduced drawing will be 10.39 inches in length and 10.39 inches in width, achieving a 56.70% reduction in length and a 71.13% reduction in width compared to the original size.
Step-by-step explanation:
Calculate the original drawing's area: Original area = length * width = 24 inches * 36 inches = 864 square inches.
Find the desired area for the reduced drawing: Desired area = 1/8 * original area = 864 square inches / 8 = 108 square inches.
Determine the side length of the reduced drawing: Since the area is a square, the side length is the square root of the desired area. Side length = √108 square inches ≈ 10.39 inches.
Calculate the percentage reduction in each dimension:
Length reduction: [(original length - reduced length) / original length] * 100% = [(24 inches - 10.39 inches) / 24 inches] * 100% ≈ 56.70%
Width reduction: [(original width - reduced width) / original width] * 100% = [(36 inches - 10.39 inches) / 36 inches] * 100% ≈ 71.13%
Therefore, Carmen's reduced drawing will be 10.39 inches by 10.39 inches, with a significant reduction in size in both dimensions.
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Complete Question
Carmen has a drawing from art class that measures 24 inches in length and 36 inches in width. She decides to scan and reduce her drawing so that the resulting area is only one-eighth (1/8) of the original. What are the dimensions, both in length and width, of Carmen's reduced drawing? Additionally, what percentage reduction does she achieve in each dimension compared to the original size?
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