Question

a triangle has sides with lengths of 19 feet, 27 feet, and 32 feet. is it a right triangle?

Explanation:

Step1: Recall the Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side. Let \(a = 19\), \(b=27\), \(c = 32\).

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

\(a^{2}+b^{2}=19^{2}+27^{2}=361 + 729=1090\)

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

\(c^{2}=32^{2}=1024\)

Step4: Compare \(a^{2}+b^{2}\) and \(c^{2}\)

Since \(1090
eq1024\) (i.e., \(19^{2}+27^{2}
eq32^{2}\))

Answer:

no