Question

a triangle has sides with lengths of 8 meters, 15 meters, and 17 meters. is it a right triangle? yes no

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side.
Let \(a = 8\), \(b = 15\), and \(c = 17\).
Calculate \(a^{2}+b^{2}\):
\(a^{2}=8^{2}=64\), \(b^{2}=15^{2}=225\), then \(a^{2}+b^{2}=64 + 225=289\).

Step2: Calculate \(c^{2}\)

\(c^{2}=17^{2}=289\).
Since \(a^{2}+b^{2}=c^{2}\), the triangle is a right - triangle.

Answer:

yes