Since we know that 24 is the longest side, we can assume that is is similar to the longest side of the first triangle. Already, we know that we have a scale factor 24:15 or 24/15. If we simplify that down, we get 8/5.
Now we can scale the other 2 sides using this scale factor. Since our scale is "large"/"small" we need to set up a proportion in the same way. That means that our proportions will look like 8/5 = x/11 and 8/5 = x/5. When we cross multiply we get 88 = 5x and 40=5x. We can solve them out to get that our side lengths are 8 and 17.6.
We can add all 3 sides together, 24 + 17.6 + 8 = P, to get P = 49.6.
To check your answer, add all sides of the first triangle together. That equals 31. Now do 49.6/31 = 8/5 (since our scale factor should come out to be 8/5, like the rest of the triangle). It should be the same. 248 = 248, so our answer is correct.