Question 515883
If a triangle has sides of length 5, 12, and 13, a similar triangle will have sides of length 5x, 12x, and 13x, where x is some positive number.  This is because with a similar triangle, all of the lengths will be multiplied by the same number.  The perimeter of this new triangle is then:

5x + 12x + 13x = 30x

We know that this new perimeter is 90, so we have an equation, which we can solve for x:

30x = 90
x = 3

So all of the side lengths are multiplied by 3.  Therefore the longest side of the new triangle is 13(3) = 39.