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

Answer 1

To find the length of the hypotenuse in a right triangle using the Pythagorean theorem, we use the formula:

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

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

In this case, the lengths of the legs are 3 ft and 1 ft. Therefore:

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

Now, to find \( c \), we take the square root of both sides:

\[ c = \sqrt{10} \]

From the options provided regarding Jerrod's calculation:

- He wrote \( c^2 = 32 + 12 \) which seems to be a mistake.
- The correct setup should have been \( c^2 = 3^2 + 1^2 \) = 9 + 1 = 10.
- It appears Jerrod did not set up the Pythagorean theorem correctly based on what you have shared.

Therefore, the correct response would be: **No, he set up the Pythagorean theorem incorrectly.**