The perimeter of a triangle is equal to the addition of its three sides.
side 1 + side 2 + side 3 = perimeter
The perimeter of a triangle is 13x + 8y, one of its sides has a length of 7x + 3y and another side length of 4x + 2y, then
(7x + 3y) + (4x + 2y) + side 3 = 13x + 8y
(7x + 4x) + (3y + 2y) + side 3 = 13x + 8y
11x + 5y + side 3 = 13x + 8y
side 3 = 13x + 8y - 11x - 5y
side 3 = (13x - 11x) + (8y - 5y)
side 3 = 2x + 3y