MathDB

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]
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]

11

Problems(1)