Question

do these 3 side lengths form a right triangle? 13, 80, and 81? no yes

Explanation:

Step1: Recall the Pythagorean theorem

For a right - triangle with side lengths \(a\), \(b\), and \(c\) (\(c\) is the longest side), \(a^{2}+b^{2}=c^{2}\).

Step2: Identify the sides

Let \(a = 13\), \(b = 80\), \(c = 81\).

Step3: Calculate \(a^{2}+b^{2}\)

\(a^{2}+b^{2}=13^{2}+80^{2}=169 + 6400=6569\).

Step4: Calculate \(c^{2}\)

\(c^{2}=81^{2}=6561\).

Step5: Compare \(a^{2}+b^{2}\) and \(c^{2}\)

Since \(6569
eq6561\) (i.e., \(13^{2}+80^{2}
eq81^{2}\)), these side lengths do not form a right - triangle.

Answer:

no