Natalia has an area rug measuring 57 inches by 41 inches which of the following exprssions can she use to find the area of the rug A. 57^2-41^2 B. 57^2+41^2 C. 49^2-8^2 D. 49^2+8^2?

Answer 1

To find the area of a rectangle, you use the formula:

\[ \text{Area} = \text{length} \times \text{width} \]

In Natalia's case, the dimensions of the rug are 57 inches and 41 inches. Thus, the area of the rug can be calculated using:

\[ A = 57 \times 41 \]

Now, let's evaluate the options you provided:

A. \(57^2 - 41^2\) - This expression represents the difference of squares and does not relate to the area of the rectangle.

B. \(57^2 + 41^2\) - This expression calculates the sum of the squares of the lengths, which also does not give the area.

C. \(49^2 - 8^2\) - This expression can be rewritten using the difference of squares formula \(a^2 - b^2 = (a-b)(a+b)\). Here, \(49^2 - 8^2\) simplifies to \((49 - 8)(49 + 8) = 41 \times 57\), which indeed equals the area of the rug.

D. \(49^2 + 8^2\) - Similar to option B, this is the sum of squares and doesn't relate to the area.

Based on this analysis, the correct expression that Natalia can use to find the area of the rug is:

C. \(49^2 - 8^2\).

Answer 2

Are you sure

Answer 3

Yes, let's double-check the reasoning for clarity:

1. To find the area of a rectangle, the formula is: \[ \text{Area} = \text{length} \times \text{width} \] For Natalia's rug, the dimensions are 57 inches and 41 inches, so: \[ \text{Area} = 57 \times 41 \]

2. Now, let's analyze the options again:

   • A. \(57^2 - 41^2\): This expression does not equal the area. However, it can be factored as \((57 - 41)(57 + 41)\), which equals \(16 \times 98\) and is not directly related to finding the area.

   • B. \(57^2 + 41^2\): This calculates the sum of the squares and does not represent the area of the rectangle.

   • C. \(49^2 - 8^2\): This can be factored using the difference of squares: \[ 49^2 - 8^2 = (49 - 8)(49 + 8) = 41 \times 57 \] This expression correctly gives us the product \(41 \times 57\), which equals the area of the rug.

   • D. \(49^2 + 8^2\): Similar to option B, this expression does not represent the area.

Therefore, upon reviewing, C. \(49^2 - 8^2\) is indeed the correct expression that can be used to find the area of the rug, as it simplifies to \(57 \times 41\). Thank you for prompting the re-evaluation!