Let's let the final length of the triangle be equal to x. By the Triangle inequality,

24+49>x

24+x>49

49+x>24.

The first inequality gives us the equation x<73. The second equation gives up x>25. The final equation gives up x>-25. From these equations, we know that 25 <73. So the smallest possible length of x is 26. So the perimeter of the triangle is 26+24+49=99.

And now we're done! Hope this helped!