Question

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

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

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

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

\(c^{2}=34^{2}=1156\)

Step4: Compare

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

Answer:

yes