Question

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

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

\(28^2 = 784\), \(96^2 = 9216\), so \(28^2 + 96^2 = 784 + 9216 = 10000\).

Step3: Calculate \(c^2\)

\(100^2 = 10000\).

Step4: Compare

Since \(28^2 + 96^2 = 100^2\), the triangle satisfies the Pythagorean theorem.

Answer:

yes