To assess the correctness of Rosanna's calculation using the Pythagorean theorem and the provided information, let’s review the fundamental concept of the theorem.
The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two legs (a and b) equals the square of the length of the hypotenuse (c). The formula can be expressed as:
\[ c^2 = a^2 + b^2 \]
In this case, if we have legs of lengths 12 inches and 9 inches, we can calculate the hypotenuse (c) as follows:
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Calculate the squares of the legs:
- \( 12^2 = 144 \)
- \( 9^2 = 81 \)
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Add these values:
- \( 144 + 81 = 225 \)
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Now take the square root to find the hypotenuse:
- \( c = \sqrt{225} = 15 \) inches
If Rosanna calculated that the length of c is 225 inches, she did not follow the correct steps of the Pythagorean theorem, as her answer should be the square root of that sum, not the sum itself.
Given all this information, the correct response to indicate what needs to be corrected in Rosanna's calculation is:
- Rosanna mistakenly added the squared hypotenuse with the square of the longest leg instead of adding both squared legs.
It's clear that she misidentified the results of her squaring and summing process.