Hans wanted to find the length of the hypotenuse of the right triangle. Which statement correctly identifies his error? 92+402=c2 81+80=c2 161=c2 161−−−√%C2%A0cm%C2%A0=%C2%A0c (1 point) Responses He did not finish the problem. He should have divided 161 by 2 to find the square root. He did not finish the problem. He should have divided 161 by 2 to find the square root. He did not square 40, he just multiplied by 2. He did not square 40, he just multiplied by 2. He should have added 9 + 9 to find the value of%C2%A092 . He should have added 9 + 9 to find the value of%C2%A09 squared. He should have subtracted the two squares to get%C2%A0402−92=c2 %C2%A0because numbers get too large if both legs are squared and then added together. He should have subtracted the two squares to get%C2%A040 squared minus 9 squared is equal to c squared%C2%A0because numbers get too large if both legs are squared and then added together. Skip to navigation

Question

Hans wanted to find the length of the hypotenuse of the right triangle. Which statement correctly identifies his error?    92+402=c2  81+80=c2  161=c2  161−−−√%C2%A0cm%C2%A0=%C2%A0c  (1 point) Responses  He did not finish the problem. He should have divided 161 by 2 to find the square root. He did not finish the problem. He should have divided 161 by 2 to find the square root.  He did not square 40, he just multiplied by 2. He did not square 40, he just multiplied by 2.  He should have added 9 + 9 to find the value of%C2%A092 . He should have added 9 + 9 to find the value of%C2%A09 squared.  He should have subtracted the two squares to get%C2%A0402−92=c2 %C2%A0because numbers get too large if both legs are squared and then added together. He should have subtracted the two squares to get%C2%A040 squared minus 9 squared is equal to c squared%C2%A0because numbers get too large if both legs are squared and then added together. Skip to navigation

GPT-4o mini · Answer

The correct statement that identifies Hans's error is: He did not square 40, he just multiplied by 2.

In the Pythagorean theorem, the correct method to find the length of the hypotenuse \(c\) is to square both legs of the triangle and then add them together. It seems that Hans made an error in calculating \(40^2\) and instead inaccurately performed a different operation.

For a right triangle with legs of lengths 9 and 40, the correct formula should be:

\[ 9^2 + 40^2 = c^2 \]

Calculating that gives:

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

So, the process that should have been followed involves squaring the lengths, not just multiplying.