Use same-length line segments to solve for x and y.
... PS = SR
... 4x +4 = 7x -17
... 21 = 3x . . . . . . . . . add 17-4x
... 7 = x . . . . . . . . . . . divide by 3
... PS = SR = 4·7+4 = 32
... PQ = QR
... 5y -31 = 2y +5
... 3y = 36 . . . . . . . . . add 31-2y
... y = 12 . . . . . . . . . . . divide by 3
... PQ = QR = 2·12 +5 = 29
... PT = TR = 6·7-2·12 = 18