Ariel completed the work below to show that a triangle with side lengths 9, 15, and 12 do not form a right triangle. 92+152=122 81+225=144 306≠144 Is Ariel's work correct? Why or why not? NOTE: On the sample work, this is a multiple choice question, but on the test, you will be asked to explain your answer in complete sentences. Think about WHY she is right or wrong when completing this question, so you are prepared for the test. (1 point) Responses No, when setting up the Pythagorean Theorem, the longest side needs to be by itself. No, when setting up the Pythagorean Theorem, the longest side needs to be by itself. Yes, Ariel's work is correct and this is not a right triangle. Yes, Ariel's work is correct and this is not a right triangle. No, she squared the numbers instead of multiplying each of them by 2. No, she squared the numbers instead of multiplying each of them by 2. Yes, Ariel's work is correct and this is a right triangle. Yes, Ariel's work is correct and this is a right triangle. Skip to navigation

Answer 1

Ariel's work is not correct because she did not identify the longest side correctly when applying the Pythagorean theorem. For a triangle to be a right triangle, the square of the length of the longest side must equal the sum of the squares of the lengths of the other two sides.

In this case, the side lengths are 9, 12, and 15, and the longest side is 15, not 12. Therefore, the correct application of the Pythagorean theorem should be:

\( 9^2 + 12^2 = 15^2 \)

Calculating these values gives:

\( 9^2 = 81 \)
\( 12^2 = 144 \)
\( 15^2 = 225 \)

Now, we check if the equation holds:

\( 81 + 144 = 225 \)

Since both sides are equal, we see that the triangle with side lengths 9, 12, and 15 actually forms a right triangle. Thus, Ariel's conclusion that these lengths do not form a right triangle is incorrect.