use pythagorean's theorem (a^2+b^2=c^2) to find that 10^2 + 24^2 = y plus the hypotenuse of the smaller right triangle (call it g). using the theorem and the well known pythagorean triple, the bigger triangle is a variation of a 5,12,13 triangle (multiples by two) so the bigger triangle's hypotenuse is 26. because the triangles are similar and in a 4:10/2:5 ratio, we know that x:24 is 2:5, making x 9.6. using pythagorean's theorem again, we find that the hypotenuse of the smaller triangle is 10.4. since we know y+g = 26, and we now know that g=10.4, y=26-10.4, making y 15.6.
TL;DR: y=15.6 and x=9.6
