the triangles are similar so that means there is a constant ratio for each side length. so comparing the ratios from the bigger triangle to the smaller triangle, leaves us with 9/3 and 15/5. if you take those and divide them you get 3 for both of them which is the constant. so then in order to find the length of AB just take the side length of XY (6) and divide it by 3 (the constant ratio) and there you have your answer!
this creates a polygon which can be shortened to be a triangle with side lengths 3 and 4 and the hypotenuse unknown. to find the side length you use the formula a^2 + b^2 = c^2
