To determine which option is correct regarding Rosanna's calculation of the length \( c \), we need to consider what the Pythagorean Theorem states. The Pythagorean Theorem is given by the formula:
\[ c^2 = a^2 + b^2 \]
where \( c \) is the hypotenuse, and \( a \) and \( b \) are the other two sides of a right triangle.
From the provided responses, the main focus should be on how Rosanna arrived at her answer. Here are the responses evaluated:
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Rosanna mistakenly added the squared hypotenuse with the square of the longest leg instead of adding both squared legs.
- This indicates a misunderstanding of the theorem, but it does not specify if she computed \( c \) correctly.
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Rosanna should take the square root of the sum when using the Pythagorean Theorem.
- This is important because after calculating \( a^2 + b^2 \), she should take the square root to find \( c \). If she ended with a squared value without taking the square root, that would indicate an error.
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Rosanna forgot to divide the answer she found through the Pythagorean Theorem by 2.
- This is not correct in the context of the Pythagorean Theorem, as there is no step involving division by 2.
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Rosanna’s answer is right because she correctly applied the Pythagorean Theorem.
- This would only be true if she properly computed \( c \) using the theorem.
Given that Rosanna calculated \( c \) to be 225 inches and if this indeed is the hypotenuse, the error could be that she did not take the square root of the sum \( a^2 + b^2 \).
Therefore, the most accurate response that indicates what needs to be corrected in her calculation is:
Rosanna should take the square root of the sum when using the Pythagorean Theorem.
9 answers