Question

a triangle with sides of lengths 9, 22, and 24 is a right triangle
a. true
b. false

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with sides \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Let \(a = 9\), \(b = 22\) and \(c = 24\) (assuming the longest side is the hypotenuse).

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

\(a^{2}+b^{2}=9^{2}+22^{2}=81 + 484=565\).

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

\(c^{2}=24^{2}=576\).

Step4: Compare results

Since \(565
eq576\), \(a^{2}+b^{2}
eq c^{2}\).

Answer:

B. False