Question

do these 3 side lengths form a right triangle? 13, 80, and 81?

Explanation:

Step1: Recall Pythagorean theorem

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

Step2: Identify the sides

Let \(a = 13\), \(b = 80\), and \(c = 81\). Calculate \(a^{2}+b^{2}\) and \(c^{2}\).
\[a^{2}=13^{2}=169\]
\[b^{2}=80^{2}=6400\]
\[a^{2}+b^{2}=169 + 6400=6569\]
\[c^{2}=81^{2}=6561\]

Step3: Compare

Since \(a^{2}+b^{2}=6569
eq6561 = c^{2}\), the three side - lengths do not form a right - triangle.

Answer:

no