Question

a triangle has sides with lengths of 13 yards, 16 yards, and 20 yards. is it a right triangle? yes no

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with sides \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here, \(c\) is the longest side. So \(a = 13\), \(b = 16\) and \(c = 20\).

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

\(a^{2}+b^{2}=13^{2}+16^{2}=169 + 256=425\).

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

\(c^{2}=20^{2}=400\).

Step4: Compare

Since \(a^{2}+b^{2}=425
eq400 = c^{2}\), the triangle is not a right - triangle.

Answer:

no