To find the area of a rectangle, you use the formula:
\[ \text{Area} = \text{length} \times \text{width} \]
For Natalia's area rug, the length and width are given as 57 inches and 41 inches, respectively. Therefore, the area can be calculated as:
\[ \text{Area} = 57 \times 41 \]
Now, we need to examine the options provided to determine which expression relates to calculating the area.
A. \(49^2 + 8^2\): This does not correspond to the rectangle's dimensions.
B. \(57^2 - 41^2\): Using the difference of squares formula, this expression simplifies to \((57 - 41)(57 + 41)\), which does not directly give the area.
C. \(49^2 - 8^2\): Similar to option B, this does not seem to relate correctly to the dimensions provided.
D. \(57^2 + 41^2\): This expression adds the squares of the dimensions, which does not provide the area.
None of the provided options directly give the area \(57 \times 41\). Since the area can indeed be calculated but not by any of the available expressions in the options, we conclude that:
None of the given expressions (A, B, C, D) can be used to find the area of Natalia's rug.
However, if we strictly needed to identify an expression closest to any mathematical manipulation relating to the dimensions, none of the options satisfy the requirement to find the area of the rug directly.
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