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?

c^(2) = 3^(2) + 1^(2)
c^(2) = 9+1
c^(2) = 8
c = \sqrt(8)

No, he subtracted 1 and 9 instead of adding.
Yes, he correctly calculated the length of the hypotenuse.
No, he made an error finding the square root.
No, he set up the Pythagorean theorem incorrectly.

Answer 1

Let’s analyze Jerrod's calculations according to the Pythagorean theorem, which is given by \( c^2 = a^2 + b^2 \).

In this case, the legs of the triangle are 3 ft and 1 ft. So we have:

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

Jerrod originally calculated:

1. Setting up the equation correctly (which he did).
2. The calculation \( c^2 = 9 + 1 = 8 \) is incorrect. The correct answer should be \( c^2 = 10 \).

Therefore, he did have an error in the addition step, as he incorrectly summed \( 3^2 + 1^2 \).

So the correct answer is: **No, he set up the Pythagorean theorem incorrectly.** Specifically, he made an error in the addition step.