Hank wanted to find the length of the hypotenuse of the right triangle. Which statement correctly identifies his error? c 40 cm 9 cm

Question

92+c2=402

81+c2=1600

1519=c2

1519−−−−√ cm = c
(1 point)
Responses
He did not set up the Pythagorean Theorem correctly. The hypotenuse should be isolated on one side of the equation.
He did not set up the Pythagorean Theorem correctly. The hypotenuse should be isolated on one side of the equation.
He did not square 9, he just multiplied by 2.
He did not square 9, he just multiplied by 2.
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 added 9 + 9 to find the value of 92

Answer 1

The correct identification of Hank's error is: He did not set up the Pythagorean Theorem correctly. The hypotenuse should be isolated on one side of the equation.

In a right triangle, according to the Pythagorean Theorem, the relationship between the lengths of the sides is given by the equation \( a^2 + b^2 = c^2 \), where \( c \) is the length of the hypotenuse. In Hank's case, the correct setup should have been:

\[ 9^2 + (40 , \text{cm})^2 = c^2 \]

Which translates to:

\[ 81 + 1600 = c^2 \]

Thus:

\[ c^2 = 1681 \]

And then \( c = \sqrt{1681} \), which gives the correct hypotenuse length.