Question

a triangle has sides with lengths of 3 feet, 4 feet, and 5 feet. is it a right triangle?

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side.
Let \(a = 3\), \(b = 4\), and \(c = 5\).
Calculate \(a^{2}+b^{2}\):
\(a^{2}=3^{2}=9\), \(b^{2}=4^{2}=16\), so \(a^{2}+b^{2}=9 + 16=25\).
Calculate \(c^{2}\):
\(c^{2}=5^{2}=25\).
Since \(a^{2}+b^{2}=c^{2}\) (i.e., \(25 = 25\)).

Answer:

yes