Question

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

c2=32+12

c2=9+1

c2=8

c=8–√

(1 point)
Responses

No, he set up the Pythagorean theorem incorrectly.
No, he set up the Pythagorean theorem incorrectly.

Yes, he correctly calculated the length of the hypotenuse.
Yes, he correctly calculated the length of the hypotenuse.

No, he made an error finding the square root.
No, he made an error finding the square root.

No, he subtracted 1 and 9 instead of adding.

Answer 1

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.**