To determine if Jerrod's calculation of the hypotenuse is correct, we will apply the Pythagorean theorem, which states that for a right triangle with legs of lengths \( a \) and \( b \), and hypotenuse \( c \):
\[ c^2 = a^2 + b^2 \]
Here, the lengths of the legs are 3 ft and 1 ft.
Calculating the squares:
\[ c^2 = 3^2 + 1^2 \] \[ c^2 = 9 + 1 \] \[ c^2 = 10 \]
To find \( c \), we take the square root of both sides:
\[ c = \sqrt{10} \]
Now let's analyze Jerrod's work:
- He wrote \( c^2 = 9 + 1 \), which is correct.
- However, he seems to have stated that \( c^2 = 8 \) in his process, which is incorrect. The correct addition is \( 10 \).
- Lastly, when he tried to find \( c \), he wrote \( c = 8 - \sqrt{???} \), which does not make sense.
Given this analysis, Jerrod made errors in two steps:
- He did not sum the squares correctly.
- He miscalculated the square root aspect.
So the correct response is: No, he set up the Pythagorean theorem incorrectly.