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

Question

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

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 finish the problem. He should have divided 1618 by 2 to find the square root.

Answer 1

The correct statement that identifies Hans' error is:

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

This statement captures the essence of the mistake; Hans did not correctly compute the squares of the side lengths. Specifically, 9 squared should be calculated as \(9^2 = 81\), not just treated as the sum of 9 and 9. However, it's worth noting that the correct calculation for the hypotenuse in the Pythagorean theorem involves squaring the lengths and then adding them, which he incorrectly asserted as \(92 + 402\) (which should have been \(9^2 + 40^2\)).

If we are to highlight more precisely:

• The leg lengths should have been squared individually as \(9^2 = 81\) and \(40^2 = 1600\), yielding \(81 + 1600 = 1681\) for \(c^2\), leading to the hypotenuse \(c = \sqrt{1681}\), not 1618.

Therefore, there is ambiguity in some of the options you provided. The most directly related option regarding squaring is that he miscalculated the square of 9.

Answer 2

whats the closest answer

Answer 3

The closest answer to identifying Hans' error is:

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

While this statement is a bit misleading in its wording, it aims to highlight that Hans incorrectly handled the squaring of the side lengths. His calculation was flawed because he either didn't square 9 correctly or he mismanaged the squaring process in general, which resulted in an incorrect summation in his setup of the Pythagorean theorem.

In the context provided, this answer captures the essence of the error most accurately compared to the other options.

Answer 4

which answer

Answer 5

Given the options provided, the answer that is closest to identifying Hans' error is:

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

This is because Hans should have squared 9 (which equals 81) rather than treating it incorrectly. This option acknowledges the mistake in squaring the value of one of the legs of the triangle.