Question

Please someone help me. This is 3rd time I'm posting this question. No absurd answer please. The question clearly says show that the ration is 1+root5 over 2. The topic is quadratics. Picture attached.

Answer 1

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