In an isosceles right-angled triangle AOB, points P; Q and S are chosen on sides OB, OA, and AB respectively such that a square PQRS is formed as shown. If the lengths of OP and OQ are a and b respectively, and the area of PQRS is 2 5 that of triangle AOB, determine a : b. [asy][asy] pair A = (0,3); pair B = (0,0); pair C = (3,0); pair D = (0,1.5); pair E = (0.35,0); pair F = (1.2,1.8); pair J = (0.17,0); pair Y = (0.17,0.75); pair Z = (1.6,0.2); draw(A--B); draw(B--C); draw(C--A); draw(D--F--Z--E--D); draw("$O$", B, dir(180)); draw("$B$", A, dir(45)); draw("$A$", C, dir(45)); draw("$Q$", E, dir(45)); draw("$P$", D, dir(45)); draw("$R$", Z, dir(45)); draw("$S$", F, dir(45)); draw("$a$", Y, dir(210)); draw("$b$", J, dir(100)); [/asy][/asy]