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

40 cm, c, 9 cm

9^2 + 40^2 - c^2
81 + 80 = c^2
161 = c^2
\/161 = c
Responses

He did not finish the problem. He should have divided 161 by 2 to find the square root.

He should have subtracted the two squares to get 40^2 - 9^2 = c^2 too large if both legs are squared and then added together.

He did not square 40, he just multiplied by 2.

He should have added 40 + 40 to find the value of 40^2
.

1 answer

The correct identification of Hans's error in finding the hypotenuse \( c \) of the right triangle is:

He did not square 40, he just multiplied by 2.

Here's why:

When Hans wrote \( 9^2 + 40^2 - c^2 \), he incorrectly handled the calculations leading to the final expression. The correct calculation for finding the hypotenuse \( c \) in a right triangle is given by the Pythagorean theorem:

\[ c^2 = a^2 + b^2 \] where \( a \) and \( b \) are the lengths of the legs of the triangle. In this case, \( a = 9 \) cm and \( b = 40 \) cm:

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

Calculating this gives:

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

Hans’s error mainly stems from either misunderstanding the formula or miscalculating when trying to apply it.