To find the area of the rug, Natalia can use the formula for the area of a rectangle, which is given by:
\[ \text{Area} = \text{length} \times \text{width} \]
In this case, the dimensions of the rug are 57 inches and 41 inches. Therefore, the area can be calculated as:
\[ \text{Area} = 57 \times 41 \]
None of the options provided directly compute the area in this way, but we can analyze the provided expressions.
- A. \(57^2 - 41^2\): This is a difference of squares, which doesn't apply here.
- B. \(57^2 + 41^2\): This sums the squares of the dimensions, which doesn't represent area.
- C. \(49^2 - 8^2\): This can be factored as \((49 - 8)(49 + 8)\) = \(41 \times 57\).
- D. \(49^2 + 8^2\): This sums the squares of 49 and 8, which also doesn't represent area.
The expression that can be used to find the area of the rug is:
C. \(49^2 - 8^2\)
This is equivalent to calculating \(41 \times 57\).
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