Ariel completed the work below to show that a triangle with side lengths 13, 12, and 5 do not form a right triangle.

Question

12 2+13 2=5 2


144+169=25


313≠25


Is Ariel's work and answer correct? Why or why not?



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.

(4 points)

Answer 1

Ariel's work contains a mistake in the initial application of the Pythagorean theorem. The Pythagorean theorem states that for a triangle to be a right triangle, the square of the lengths of the two shorter sides must equal the square of the length of the longest side. In this case, the side lengths are 13, 12, and 5, with 13 being the longest side.

The correct application of the theorem should be:

12² + 5² = 13²

Calculating this gives:

144 + 25 = 169

Since 169 = 169, the equation holds true, which means that the triangle with sides 12, 5, and 13 does form a right triangle. Therefore, Ariel's conclusion that these sides do not form a right triangle is incorrect. The proper reasoning should recognize that the sum of the squares of the lengths of the two shorter sides equals the square of the length of the longest side, confirming that it is indeed a right triangle.