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

Question

c^2 = 3^2+1^2
c^2 =9+1
c^2 = 8
c = V8
(1 point)
• No, he set up the Pythagorean theorem incorrectly.
• 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.

Answer 1

Jerrod correctly set up the Pythagorean theorem and performed the calculations accurately up to the point where he expressed the length of the hypotenuse. Here’s the breakdown:

1. He correctly used the Pythagorean theorem: \( c^2 = a^2 + b^2 \), where \( a = 3 \) ft and \( b = 1 \) ft.

2. He calculated \( c^2 = 3^2 + 1^2 \) correctly as: \[ c^2 = 9 + 1 = 10 \] However, Jerrod wrote \( c^2 = 8 \), which is incorrect; the correct sum should be \( c^2 = 10 \).

3. So, he made a mistake in adding the squares of the legs, but he got it right when he used the formula for the square root. The correct calculation for \( c \) should be: \[ c = \sqrt{10} \]

Based on this analysis, the best answer is: No, he set up the Pythagorean theorem incorrectly.