Question

a triangle has sides with lengths of 16 centimeters, 30 centimeters, and 34 centimeters. 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 \(a = 16\), \(b = 30\), and \(c = 34\).

Step2: Calculate \(a^{2}+b^{2}\)

\(a^{2}=16^{2}=256\), \(b^{2}=30^{2}=900\). Then \(a^{2}+b^{2}=256 + 900=1156\).

Step3: Calculate \(c^{2}\)

\(c^{2}=34^{2}=1156\).
Since \(a^{2}+b^{2}=c^{2}\), the triangle is a right - triangle.

Answer:

yes