Question

1. in a triangle with sides 6, 8, and 10, is this a right triangle? a. sometimes b. yes c. cannot be determined d. no

Explanation:

Step1: Recall Pythagorean theorem

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

Step2: Identify sides

Let \(a = 6\), \(b = 8\), and \(c = 10\).

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

\(a^{2}=6^{2}=36\), \(b^{2}=8^{2}=64\), so \(a^{2}+b^{2}=36 + 64=100\). And \(c^{2}=10^{2}=100\).

Step4: Check the theorem

Since \(a^{2}+b^{2}=c^{2}\), it is a right - triangle.

Answer:

B. Yes