Question

a triangle has sides with lengths of 96 kilometers, 100 kilometers, and 28 kilometers. 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 \(a = 28\), \(b = 96\), and \(c = 100\).

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

\(a^{2}=28^{2}=784\), \(b^{2}=96^{2}=9216\). Then \(a^{2}+b^{2}=784 + 9216=10000\).

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

\(c^{2}=100^{2}=10000\).

Step4: Compare

Since \(a^{2}+b^{2}=c^{2}\) (i.e., \(10000 = 10000\)), the triangle is a right - triangle.

Answer:

yes