Golden Rectangles: construct a golden rectangle using an 8.5x11'' piece of paper with 11 being the desired length

NewMindRespect

New member
Please excuse my inability to figure this one out! I am sure it is very simple, although I just don't understand the proportion as it is not what I typically see and use in the very basic college math I take. The "golden ratio" is, Phi=1.61803. I am supposed to construct a golden rectangle using an 8.5x11'' piece of paper with 11 being the desired length (l) for the golden rectangle and solve for the width using the following proportion:

l/w=11/w=1.61803

Do I divide? 1.61803/11? The goal is to use the cut piece of paper (to proper proportion) and find "golden rectangles" throughout my home that are close in proportion. Thank you very much in advance!

Subhotosh Khan

Super Moderator
Staff member
Let's do some simpler problems!

Let's assume that the golden ratio is 11. In that case what would be the width of your rectangle from the 8.5 by 11 paper (and the length stays = 11)?

Let's assume that the golden ratio is 2. In that case what would be the width of your rectangle from the 8.5 by 11 paper (and the length stays = 11)?

Are you getting some ideas about the answer to your question?

NewMindRespect

New member
I believe with that being posed, I would set the proportion as 11/1=8.5/2???

Otis

Senior Member
… I would set the proportion as 11/1=8.5/2
11 cannot be half of 8.5

Denis

Senior Member
I believe with that being posed, I would set the proportion as 11/1=8.5/2???
11/x = 8.5/2
8.5x = 22
x = 22/8.5 = 44/17

Jomo

Elite Member
11/x = 8.5/2
8.5x = 22
x = 22/8.5 = 44/17
Nicely done, you are improving.

Denis

Senior Member
Thank you Mr.Pope !!