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.