Question

a triangle has sides with lengths of 16 yards, 20 yards, and 12 yards. is it a right triangle? yes no

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side.
Let \(a = 12\), \(b = 16\), and \(c = 20\).

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

\(a^{2}+b^{2}=12^{2}+16^{2}=144 + 256=400\)

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

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

Step4: Compare

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

Answer:

yes