Let's analyze Jerrod's calculations step by step using the Pythagorean theorem, which states that for a right triangle with legs of length \( a \) and \( b \), and hypotenuse \( c \):
\[ c^2 = a^2 + b^2 \]
In this case, the legs of the triangle are 3 ft and 1 ft:
\[ c^2 = 3^2 + 1^2 \]
Calculating the squares:
\[ c^2 = 9 + 1 \]
This simplifies to:
\[ c^2 = 10 \]
Now, to find \( c \), we take the square root:
\[ c = \sqrt{10} \]
Now, let's look at Jerrod's steps:
- He wrote \( c^2 = 3^2 + 1^2 \).
- He incorrectly wrote \( c^2 = 9 + 1 \).
- Then, he made an incorrect statement that \( c^2 = 8 \) (which is wrong; it should be 10).
- Finally, he wrote \( c = 8 - \sqrt{\) (this seems like a typographical error).
Based on this analysis, Jerrod made multiple mistakes:
- He did not calculate the correct sum of the squares correctly (he should have gotten 10, but said 8).
- He also did not apply the square root correctly.
Thus, the correct response is: No, he set up the Pythagorean theorem incorrectly.