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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 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 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 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.
Remaining Attempts : 3

Answer 1

To find the hypotenuse \( c \) of a right-angled triangle using the Pythagorean Theorem, the correct formula is:

\[ c = \sqrt{a^2 + b^2} \]

where \( a \) and \( b \) are the lengths of the legs of the triangle. In this case, the legs are 9 inches and 12 inches.

Calculating this step by step:

1. Calculate \( a^2 \): \[ 9^2 = 81 \]

2. Calculate \( b^2 \): \[ 12^2 = 144 \]

3. Add the squares: \[ 81 + 144 = 225 \]

4. Take the square root: \[ c = \sqrt{225} = 15 \text{ inches} \]

Since Rosanna calculated \( c \) to be 225 inches, she likely squared the sum instead of taking the square root. Therefore, the correct response would be:

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