Question

a triangle has sides with lengths of 18 inches, 24 inches, and 30 inches. 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 \(a = 18\), \(b = 24\), and \(c = 30\).

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

\(a^{2}=18^{2}=324\), \(b^{2}=24^{2}=576\). Then \(a^{2}+b^{2}=324 + 576=900\).

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

\(c^{2}=30^{2}=900\).

Step4: Compare

Since \(a^{2}+b^{2}=c^{2}\) (i.e., \(900 = 900\)), it is a right - triangle.

Answer:

yes