Let's analyze Jerrod's calculations step by step according to the Pythagorean theorem, which 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 (legs \( a \) and \( b \)):
\[ c^2 = a^2 + b^2 \]
Given values:
- \( a = 3 \) ft
- \( b = 1 \) ft
Substituting these values into the Pythagorean theorem:
\[ c^2 = 3^2 + 1^2 \] \[ c^2 = 9 + 1 \] \[ c^2 = 10 \]
Now, to find \( c \):
\[ c = \sqrt{10} \]
Now, let's address Jerrod's work:
- He wrote \( c^2 = 32 + 12 \), which is incorrect since the legs are 3 and 1 (not 32 and 12).
- Then he wrote \( c^2 = 9 + 1 \) which is correct.
- However, when he stated \( c^2 = 8 \), that is a mistake, as \( c^2 = 10 \).
Finally, he wrote \( c = 8 - \sqrt{} \), which does not make sense in terms of this problem.
Given this information, the correct answer is:
No, he set up the Pythagorean theorem incorrectly.