So you remember that the Pythagorean theorem is the length of one leg squared plus the leg of the other leg squared equals the hypotenuse squared, right? and you know the the hypotenuse has to be the longest side in a right triangle.
All you have to do here is figure out if
[tex] {7}^{2} + {24}^{2} = {25}^{2} [/tex]
[tex] {7}^{2} = 49[/tex]
[tex] {24}^{2} = 576[/tex]
[tex]49 + 576 = 625[/tex]
[tex] \sqrt{625} = 25[/tex]
So yes, a triangle with those side lengths would be a right triangle because the Pythagorean theorem is true.
