Areil completed the work below to show that a triangle with side lengths 5, 4, and 3 do not form a right triangle.

Question

5^2 + 4^2 = 3^2

25 + 16 = 9

41 =/ 9
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.

Answer 1

Ariel's work contains errors in both the analysis and calculations. To determine if a triangle with side lengths 5, 4, and 3 forms a right triangle, we should apply the Pythagorean theorem, which states that for any right triangle, the sum of the squares of the lengths of the two shorter sides should equal the square of the length of the longest side.

In this case, the side lengths are 5, 4, and 3, where the longest side is 5. Therefore, we should check:

\(3^2 + 4^2 = 5^2\)

Calculating this gives:

\(3^2 = 9\)
\(4^2 = 16\)
\(5^2 = 25\)

Now, add the squares of the two shorter sides:

\(9 + 16 = 25\)

Since \(25 = 25\), this shows that the triangle with these sides does indeed form a right triangle. Therefore, Ariel's conclusion that the triangle does not form a right triangle is incorrect. The correct analysis demonstrates that the triangle with sides 5, 4, and 3 is a right triangle.