Question

a triangle has sides with lengths of 26 feet, 10 feet, and 24 feet. is it a right triangle? yes no

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with sides \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side. Here \(a = 10\), \(b = 24\) and \(c = 26\).

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

\(a^{2}+b^{2}=10^{2}+24^{2}=100 + 576=676\)

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

\(c^{2}=26^{2}=676\)

Step4: Compare results

Since \(a^{2}+b^{2}=c^{2}\) (i.e., \(676 = 676\)), the triangle is a right - triangle.

Answer:

yes