To determine if Jerrod's answer is correct, we need to check his setup of the Pythagorean theorem and his calculations.
The Pythagorean theorem states that in a right triangle:
\[ c^2 = a^2 + b^2 \]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the two legs of the triangle.
In this case, the legs \( a \) and \( b \) are 3 ft and 1 ft. According to the theorem:
\[ c^2 = 3^2 + 1^2 \] \[ c^2 = 9 + 1 \] \[ c^2 = 10 \]
Next, to find \( c \), we take the square root of both sides:
\[ c = \sqrt{10} \]
Jerrod wrote:
\[ c^2 = 3^2 + 1^2 \] \[ c^2 = 9 + 1 \] \[ c^2 = 8 \] \[ c = \sqrt{8} \]
Here, he made a mistake in the addition. The sum of \( 9 + 1 \) is \( 10 \), not \( 8 \).
So the correct calculations show that:
- The correct setup is \( c^2 = 3^2 + 1^2 \).
- The correct result is \( c^2 = 10 \) and \( c = \sqrt{10} \).
Jerrod's answer is therefore incorrect because he set up the Pythagorean theorem incorrectly by computing \( 9 + 1 \) as \( 8 \).
The correct response is: "No, he set up the Pythagorean theorem incorrectly."