2 of 202 of 20 Items Question 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 Yes, Ariel's work is correct and this is a right triangle. Yes, Ariel's work is correct and this is 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. 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.

Answer 1

Yes, Ariel's work is correct and this is not a right triangle.

In her calculations, Ariel applied the Pythagorean Theorem, which states that for a triangle to be a right triangle, the square of the length of the longest side (the hypotenuse) must equal the sum of the squares of the lengths of the other two sides. In this case, the longest side is 15.

Ariel calculated:

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

Since the two sides equal each other, she concluded incorrectly in her work as stated. The correct setup would show if 9, 12, and 15 form a triangle.

Thus, checking if 9, 15, or 12 is the longest side and adjusting correctly shows \(9^2 + 12^2 = 15^2\). Since she established 15 as the hypotenuse, her reasoning behind the values was correct; however, she neglected the correct association of the squared values. Thus, it confirms that 9, 12, and 15 indeed do form a right triangle.

Correction: 15 is indeed the longest side, 225 = 225 thus is indeed a right triangle.