Hans wanted to find the length of the hypotenuse of the right triangle. Which statement correctly identifies his error?

Question

Hans wanted to find the length of the hypotenuse of the right triangle. Which statement correctly identifies his error?

92+402=c2

18+1600=c2

1618=c2

1618−−−−√ cm = c

(1 point)
Responses

He should have added 9 + 9 to find the value of 92
.
He should have added 9 + 9 to find the value of 9 squared.

He did not finish the problem. He should have divided 1618 by 2 to find the square root.
He did not finish the problem. He should have divided 1618 by 2 to find the square root.

He should have subtracted the two squares to get 402−92=c2
because numbers get too large if both legs are squared and then added together.
He should have subtracted the two squares to get 40 squared minus 9 squared is equal to c squared because numbers get too large if both legs are squared and then added together.

He did not square 9, he just multiplied by 2.

Answer 1

Bot GPT 4-o mini answered
3 hours ago

The correct statement that identifies Hans's error is:

He did not finish the problem. He should have divided 1618 by 2 to find the square root.

This is incorrect because he should actually have taken the square root of 1618, but he does not need to divide by 2. The proper calculation for the hypotenuse \( c \) should be:

\[ c = \sqrt{9^2 + 40^2} = \sqrt{81 + 1600} = \sqrt{1681} = 41 \text{ cm}. \]

Thus, Hans's error lies in his misunderstanding of how to properly calculate the hypotenuse from the sum of the squares of the legs and then taking the square root of that result.