Question

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

Explanation:

Step1: Apply Pythagorean theorem

$$a^{2}+b^{2}=c^{2}$$
Let \(a = 7\), \(b = 24\), \(c = 25\)

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

\(7^{2}+24^{2}=49 + 576=625\)

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

\(25^{2}=625\)

Step4: Compare results

Since \(7^{2}+24^{2}=25^{2}\), by Pythagorean theorem, it is a right triangle.

Answer:

C. Yes