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

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

No, he subtracted 1 and 9 instead of adding.

Answer 1

To determine if Jerrod's calculation is correct, let’s analyze the steps he took using the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, \( c^2 = a^2 + b^2 \), where \( c \) is the hypotenuse, and \( a \) and \( b \) are the lengths of the legs.

In this case:
- One leg (a) is 3 ft.
- The other leg (b) is 1 ft.

Calculating the hypotenuse:

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

Now, taking the square root to find \( c \):

\[
c = \sqrt{10}
\]

Now let’s review Jerrod's work:

1. He wrote that \( c^2 = 3^2 + 1^2 \) as \( c^2 = 32 + 12 \), which is incorrect. It should have been \( c^2 = 9 + 1 \). This shows that he misrepresented the squares of the legs.
2. Correctly, it continues with \( c^2 = 10 \), but he ended with \( c^2 = 8 \).

So, to answer the question:

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

This is because he incorrectly calculated the squares and ended with an incorrect sum.