Question

a triangle has sides with lengths of 30 meters, 40 meters, and 50 meters. 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 \(a = 30\), \(b = 40\), and \(c = 50\).

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

\(a^{2}+b^{2}=30^{2}+40^{2}=900 + 1600=2500\).

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

\(c^{2}=50^{2}=2500\).
Since \(a^{2}+b^{2}=c^{2}\), the triangle is a right - triangle.

Answer:

yes