Jerrod found the length of the hypotenuse of a right triangle with legs that are 3 ft and 1 ft. Is his answer correct?

To determine if Jerrod's calculations are correct, let's review the Pythagorean theorem, which states:

\[ c^2 = a^2 + b^2 \]

where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the legs of the right triangle.

In Jerrod's case:

• One leg \(a = 3\) ft
• The other leg \(b = 1\) ft

Plugging these values into the Pythagorean theorem:

\[ c^2 = 3^2 + 1^2 \] \[ c^2 = 9 + 1 \] \[ c^2 = 10 \]

Next, we find \(c\):

\[ c = \sqrt{10} \]

Now let's analyze Jerrod's calculations:

1. He incorrectly set up the equation with: \(c^2 = 3^2 + 1^2\) as \(c^2 = 32 + 12\). This is a setup error.
2. He then wrote \(c^2 = 9 + 1\), which is correct, but he stated \(c^2 = 8\), which is incorrect.

Based on these findings, we conclude that:

• Jerrod set up the Pythagorean theorem incorrectly,
• Additionally, he made an error by concluding that \(c^2 = 8\) instead of \(c^2 = 10\).

Therefore, the correct response is:

No, he set up the Pythagorean theorem incorrectly.