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 subtracted 1 and 9 instead of adding.
No, he subtracted 1 and 9 instead of adding.

No, he made an error finding the square root.

Answer 1

Let's analyze Jerrod's calculations step by step according to the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse \( c \) is equal to the sum of the squares of the other two sides (legs \( a \) and \( b \)):

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

**Given values:**
- \( a = 3 \) ft
- \( b = 1 \) ft

Substituting these values into the Pythagorean theorem:

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

Now, to find \( c \):

\[
c = \sqrt{10}
\]

Now, let's address Jerrod's work:

- He wrote \( c^2 = 32 + 12 \), which is incorrect since the legs are 3 and 1 (not 32 and 12).
- Then he wrote \( c^2 = 9 + 1 \) which is correct.
- However, when he stated \( c^2 = 8 \), that is a mistake, as \( c^2 = 10 \).

Finally, he wrote \( c = 8 - \sqrt{} \), which does not make sense in terms of this problem.

Given this information, the correct answer is:

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