Question

1. a triangle has legs of 7 and 24 and the hypotenuse is 25. is it a right triangle? a. yes b. sometimes c. no d. cannot be determined

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs and \(c\) is the hypotenuse.

Step2: Substitute the values

Let \(a = 7\), \(b = 24\), and \(c = 25\). Calculate \(a^{2}+b^{2}\) and \(c^{2}\). \(a^{2}=7^{2}=49\), \(b^{2}=24^{2}=576\), so \(a^{2}+b^{2}=49 + 576=625\). And \(c^{2}=25^{2}=625\).

Step3: Check the equality

Since \(a^{2}+b^{2}=c^{2}\) (i.e., \(625 = 625\)), the triangle is a right - triangle.

Answer:

A. Yes