A right-angled triangle is labeled as follows: the height is labeled 9 inches; the base is labeled 12 inches; and hypotenuse is labeled c.

Question

Rosanna calculates that the length of c
is 225 in. What needs to be corrected in her calculation?

(1 point)
Responses

Rosanna forgot to divide the answer she found through the Pythagorean Theorem by 2.
Rosanna forgot to divide the answer she found through the Pythagorean Theorem by 2.

Rosanna mistakenly added the squared hypotenuse with the square of the longest leg instead of adding both squared legs.
Rosanna mistakenly added the squared hypotenuse with the square of the longest leg instead of adding both squared legs.

Rosanna’s answer is right because she correctly applied the Pythagorean Theorem.
Rosanna’s answer is right because she correctly applied the Pythagorean Theorem.

Rosanna should take the square root of the sum when using the Pythagorean Theorem.

Answer 1

To determine the correct application of the Pythagorean Theorem, we need to evaluate the situation. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):

\[ c^2 = a^2 + b^2 \]

In this case, the height and base are given as 9 inches and 12 inches, respectively. Thus, we can apply the theorem as follows:

• a = 9 inches
• b = 12 inches

Calculating:

\[ c^2 = 9^2 + 12^2 \] \[ c^2 = 81 + 144 \] \[ c^2 = 225 \]

Now taking the square root to find c:

\[ c = \sqrt{225} \] \[ c = 15 \text{ inches} \]

Rosanna calculated the hypotenuse to be 225 inches, which is incorrect.

The most appropriate correction to Rosanna's error is that she should take the square root of the sum when using the Pythagorean Theorem, since she seemed to have stated the hypotenuse as 225 inches without taking the square root of 225.

So the correct response is:

Rosanna should take the square root of the sum when using the Pythagorean Theorem.