A rectangle has width 1 unit and length x units.

A square is cut off it.

the rectangle left behind is similar to the original rectangle.

Find the value of x in surd form.

The value of x is called Golden ratio

MY attempt:

area of the original rectangle = x sq units

area of square = 1 sq units

are of b ( small rectangle) = x-1 sq units

i found the golden ratio by doing this:

since width and length are positive units

thus

I found the answer but I read off a forum that i needed to set up the equations relating ratios involving x

but when i tihnk about it why is this is the part im confused about

in my head 3 = (6/2) thus i thought for a long time that the ratio should be not

Pleqase can some explain more in order to deepen my understanding thank you