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−−−−√%C2%A0cm%C2%A0=%C2%A0c (1 point) Responses He did not square 9, he just multiplied by 2. He did not square 9, 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 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%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  18+1600=c2  1618=c2  1618−−−−√%C2%A0cm%C2%A0=%C2%A0c  (1 point) Responses  He did not square 9, he just multiplied by 2. He did not square 9, 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 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%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 identification of Hans's error is:

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

This response accurately points out that Hans didn't proceed to calculate the hypotenuse correctly after squaring the legs and summing them up. The correct approach is to take the square root of \(c^2\), rather than dividing \(1618\) by \(2\). However, it's important to clarify that he wouldn't actually divide by \(2\) at any point; he should take the square root of \(1618\) directly. So while this response indicates that he didn't complete the problem, it is misleading in the approach to finding the square root.

The accurate root should be calculated as \(c = \sqrt{1618}\) and should not involve dividing by \(2\).