Let’s evaluate Jerrod’s work step by step:
- The Pythagorean theorem states that \( c^2 = a^2 + b^2 \), where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the legs of the right triangle.
- For this triangle, the legs are given as 3 ft and 1 ft. Therefore, we can set up the equation as follows: \[ c^2 = 3^2 + 1^2 \]
- Calculating the squares: \[ c^2 = 9 + 1 \] So, \[ c^2 = 10 \]
- Taking the square root to find \( c \): \[ c = \sqrt{10} \]
Now, let’s analyze Jerrod's work:
- He started with \( c^2 = 3^2 + 1^2 \) but then wrote \( c^2 = 32 + 12 \), which is incorrect.
- His calculations show he substituted incorrectly, leading to \( c^2 = 8 \) instead of \( c^2 = 10 \).
Thus, Jerrod made mistakes in both setting up the equation and calculating it.
The correct response is: No, he set up the Pythagorean theorem incorrectly.