Questions: Just output the content of the question, DO NOT output additional information or explanations.

Just output the content of the question, DO NOT output additional information or explanations.
Transcript text: Just output the content of the question, DO NOT output additional information or explanations.
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Solution

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Solution Steps

Step 1: Identify the problem

We need to find the length of the hypotenuse of a right triangle given the lengths of the other two sides.

Step 2: Recall the Pythagorean Theorem

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b): \[ c^2 = a^2 + b^2 \]

Step 3: Substitute the given values

Here, \( a = 31 \) ft and \( b = 17 \) ft. Substitute these values into the Pythagorean Theorem: \[ c^2 = 31^2 + 17^2 \]

Step 4: Calculate the squares

\[ 31^2 = 961 \] \[ 17^2 = 289 \]

Step 5: Add the squares

\[ c^2 = 961 + 289 \] \[ c^2 = 1250 \]

Step 6: Take the square root

\[ c = \sqrt{1250} \] \[ c \approx 35.36 \]

Final Answer

The length of the hypotenuse is approximately 35.36 feet.

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