Question

a triangle has sides with lengths of 23 feet, 31 feet, and 42 feet. is it a right triangle? yes no

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with side lengths \(a\), \(b\), and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Let \(a = 23\), \(b = 31\), and \(c = 42\).

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

\(a^{2}+b^{2}=23^{2}+31^{2}=529 + 961=1490\).

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

\(c^{2}=42^{2}=1764\).

Step4: Compare results

Since \(1490
eq1764\), i.e., \(a^{2}+b^{2}
eq c^{2}\).

Answer:

no