To find the length of the hypotenuse in a right triangle using the Pythagorean theorem, we use the formula:
\[ c^2 = a^2 + b^2 \]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the legs.
In this case, the lengths of the legs are 3 ft and 1 ft. Therefore:
\[ c^2 = 3^2 + 1^2 \] \[ c^2 = 9 + 1 \] \[ c^2 = 10 \]
Now, to find \( c \), we take the square root of both sides:
\[ c = \sqrt{10} \]
From the options provided regarding Jerrod's calculation:
- He wrote \( c^2 = 32 + 12 \) which seems to be a mistake.
- The correct setup should have been \( c^2 = 3^2 + 1^2 \) = 9 + 1 = 10.
- It appears Jerrod did not set up the Pythagorean theorem correctly based on what you have shared.
Therefore, the correct response would be: No, he set up the Pythagorean theorem incorrectly.