Question

a triangle has sides with lengths of 6 kilometers, 15 kilometers, and 20 kilometers. is it a right triangle? yes no

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with sides \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Let \(a = 6\), \(b = 15\) and \(c = 20\) (assuming \(c\) is the longest side).
Calculate \(a^{2}+b^{2}\):
\(a^{2}+b^{2}=6^{2}+15^{2}=36 + 225=261\)

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

\(c^{2}=20^{2}=400\)
Since \(a^{2}+b^{2}=261
eq400 = c^{2}\), the triangle is not a right - triangle.

Answer:

no