Question

a triangle has sides with lengths of 68 feet, 32 feet, and 60 feet. 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 \(a = 32\), \(b = 60\), and \(c = 68\).

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

\(a^{2}=32^{2}=32\times32 = 1024\), \(b^{2}=60^{2}=60\times60=3600\). Then \(a^{2}+b^{2}=1024 + 3600=4624\).

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

\(c^{2}=68^{2}=68\times68 = 4624\).
Since \(a^{2}+b^{2}=c^{2}\), the triangle is a right - triangle.

Answer:

yes