Use the image to answer the question.

Question

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.

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

(1 point)
Responses

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

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 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.

Answer 1

To determine what needs to be corrected in Rosanna's calculation, we can use the Pythagorean Theorem, which states:

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

where \( c \) is the hypotenuse, and \( a \) and \( b \) are the legs of the right triangle.

In this case, the height (one leg) is 9 inches, and the base (the other leg) is 12 inches. So we can calculate as follows:

1. Calculate the squares:

   • \( a^2 = 9^2 = 81 \)
   • \( b^2 = 12^2 = 144 \)

2. Now, add the squares together:

   • \( c^2 = a^2 + b^2 = 81 + 144 = 225 \)

3. Finally, take the square root to find \( c \):

   • \( c = \sqrt{225} = 15 \) inches.

Rosanna calculated the length of \( c \) as 225 inches, which is incorrect.

The mistake made by Rosanna is that she should have taken the square root of the sum (225) to find the length of \( c \).

Therefore, the correct response is: Rosanna should take the square root of the sum when using the Pythagorean Theorem.