Question

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

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with side lengths \(a\), \(b\), and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side.
Let \(a = 12\), \(b = 16\), and \(c = 20\).
Calculate \(a^{2}+b^{2}\):
\(a^{2}=12^{2}=144\), \(b^{2}=16^{2}=256\).
\(a^{2}+b^{2}=144 + 256=400\).

Step2: Calculate \(c^{2}\)

\(c^{2}=20^{2}=400\).
Since \(a^{2}+b^{2}=c^{2}\) (i.e., \(400 = 400\)), the triangle is a right - triangle.

Answer:

yes