Question

do the following measurements form a right triangle? show proof (practice typing the information correctly)
5, 12, 13

Explanation:

Step1: Recall the Pythagorean theorem

For a triangle with side lengths \(a\), \(b\), and \(c\) (\(c\) is the longest side), if \(a^{2}+b^{2}=c^{2}\), then it is a right - triangle. Let \(a = 5\), \(b=12\), and \(c = 13\).

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

\(a^{2}+b^{2}=5^{2}+12^{2}=25 + 144=169\)

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

\(c^{2}=13^{2}=169\)

Since \(a^{2}+b^{2}=c^{2}\) (i.e., \(169 = 169\))

Answer:

Yes, the measurements \(5\), \(12\), and \(13\) form a right - triangle.