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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 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’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 find the length of the hypotenuse \( c \) in 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 other two sides of the triangle (the height and base in this case).

Here, Rosanna has the height \( a = 9 \) inches and the base \( b = 12 \) inches. First, we calculate \( a^2 \) and \( b^2 \):

\[ 9^2 = 81 \] \[ 12^2 = 144 \]

Now, adding those together:

\[ a^2 + b^2 = 81 + 144 = 225 \]

Now, to find \( c \):

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

Rosanna calculated that the length of \( c \) is 225 inches, which is incorrect. The mistake she made can be found in the following option:

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

This option correctly identifies that Rosanna did not take the square root of the sum of the squares of the legs, leading her to mistakenly report the hypotenuse length as 225 inches instead of 15 inches.