How would I solve this, considering I have no values whatsoever?

Question

I think that SQ is straight and so have tried to use Pythagoras, which leaves me with $a + b + c = ac/b$, but I don't see any values. How could I find values?

Answer 1

Notice the shorter sides of the rectangle are equal and hence $a+b=c$. Using Pythagoras, we have $$(b+c)^2+(a+b)^2=(a+c)^2 \\ (2c-a)^2+c^2=(a+c)^2 \\ 4c^2=6ac \implies \frac ac=\frac 23$$ And also $$\frac ac+\frac bc = 1\implies \frac bc =\frac 13$$ This gives $$a:b:c=2:1:3$$