Ariel completed the work below to show that a triangle with side lengths 13, 12, and 5 do not form a right triangle. 122+132=52 144+169=25 313≠25 Is Ariel's work and answer correct? Why or why not? %C2%A0 NOTE: You must answer the question in complete sentences to receive credit. You can type out your answer or upload an image of your written explanation.

Answer 1

Ariel's work is incorrect in two ways. First, the equation should use the lengths of the two longer sides squared to compare with the square of the shorter side when checking for a right triangle. In a right triangle, the Pythagorean theorem states that \(a^2 + b^2 = c^2\), where \(c\) is the length of the hypotenuse (the longest side).

In this case, the side lengths are 13, 12, and 5, with 13 being the longest. Therefore, we should check if \(12^2 + 5^2 = 13^2\):

\[ 12^2 + 5^2 = 144 + 25 = 169 \] \[ 13^2 = 169 \]

Since both sides are equal (169 = 169), this actually shows that the triangle with sides 13, 12, and 5 does form a right triangle, contrary to Ariel's conclusion.

Thus, the error lies in misunderstanding the correct application of the Pythagorean theorem, and the ultimate conclusion drawn by Ariel is incorrect.