Question

a triangle has sides with lengths of 25 kilometers, 26 kilometers, and 9 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 \(a = 9\), \(b = 25\), and \(c = 26\) (where \(c\) is the longest side).

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

\(a^{2}+b^{2}=9^{2}+25^{2}=81 + 625=706\).

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

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

Step4: Compare

Since \(706
eq676\), i.e., \(a^{2}+b^{2}
eq c^{2}\).

Answer:

no