To find the length of the hypotenuse \( c \) in a right-angled triangle using the Pythagorean Theorem, you need to use the formula:
\[ c = \sqrt{a^2 + b^2} \]
where \( a \) and \( b \) are the lengths of the two legs (height and base, in this case).
Given:
- Height = 9 inches
- Base = 12 inches
Calculating \( c \):
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Calculate \( a^2 \) and \( b^2 \):
- \( 9^2 = 81 \)
- \( 12^2 = 144 \)
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Add these values:
- \( 81 + 144 = 225 \)
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Take the square root:
- \( c = \sqrt{225} = 15 \) inches
Given that Rosanna calculated \( c \) as 225 inches, it suggests that she did not follow the correct procedure.
The correct answer to the question is:
Rosanna mistakenly added the squared hypotenuse with the square of the longest leg instead of adding both squared legs.