SOLUTION: I'm not sure how to do this question. Could you please help?: Diagram: http://imgur.com/a/7ucNQ This rectangle is a golden rectangle. – ABEF is a square. – Rectangle BCDE is si

Algebra ->  Rectangles -> SOLUTION: I'm not sure how to do this question. Could you please help?: Diagram: http://imgur.com/a/7ucNQ This rectangle is a golden rectangle. – ABEF is a square. – Rectangle BCDE is si      Log On


   

Question 1055386: I'm not sure how to do this question. Could you please help?:
Diagram: http://imgur.com/a/7ucNQ
This rectangle is a golden rectangle.
– ABEF is a square.
– Rectangle BCDE is similar to rectangle ACDF.
a) Show that a/1= 1/(a-1)
b) Find the exact value of a (which will give you the golden ratio) by completing the square.
Thanks in advanced :)
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Given the similarity between the two rectangles, that is already the justification for a%2Fy=y%2F%28a-1%29. The reason is, their similarity is given. The equation, replacing your "1" with a "y" is simply the proportion for comparing the corresponding rectangular parts.


a%28a-1%29=y%5E2
a%5E2-a-y%5E2=0
skipping trying to complete square;
a=%281%2B-+sqrt%281%2B4y%5E2%29%29%2F2, and probably want the PLUS form.