Someone me. this is 3rd time i'm posting this question. no absurd answer . the question clearly says show that the ration is 1+root5 over 2. the topic is quadratics. picture attached.

As the 2 rectangles are similar  the corresponding sides are in the same ratio

so AB/YX = AD / YB

AB = x and AD =1 Also YX = 1 and YB = x - 1 

so we have
x = 1 (x - 1)
x(x - 1) = 1

x^2 - x - 1 = 0

Solve this using the quadratic formula (or by completing the square) and you#ll get the golden ratio

Really long apparently