Since we're told triangle ABC is isosceles, we know that the triangle has two equal sides.
Since we're already given the measurements of two of the sides, there are two possible isosceles triangles that can be constructed: 15-15-20 OR 15-20-20

If we have a 15-15-20 triangle, then the perimeter = 15+15+20 = 50, in which case the two quantities are equal
If we have a 15-20-20 triangle, then the perimeter = 15+20+20 = 55, in which case Quantity A is greater

Answer: D