Golden Rectangle

[Mas]

If I cut of square from a golden rectangle, what would the relationship be between L and W if the original rectangle had length L and width W. Need to know the equation? I think it is W/L=L-W/W or L/WL+W/L.

Thanks.

 

[stapel]

If I cut of square from a golden rectangle, what would the relationship be between L and W if the original rectangle had length L and width W. Need to know the equation? I think it is W/L=L-W/W or L/WL+W/L.

I'm a bit confused. What is the exact text of the exercise and its instructions? Also, is it correct to assume that "L" stands for the length of the longer sides of the original rectangle (so you're cutting off a square with sides of length "W")?

And what "relationship" are you trying to find? You've already got a relationship for the original rectangle. Are you trying to find a relationship for the bit that's left after you remove the square?

When you reply, please include a clear listing of your thoughts and efforts so far. Thank you!

 

[Mas]

Golden rectangle

Looking for relationship between L and W. L=length and W=width. The resulting rectangle is similar to original rectangle and original rectangle has length L and width W. Need to know equation that represents relationship between L and W.
Thanks

 

[stapel]

Looking for relationship between L and W. L=length and W=width. The resulting rectangle is similar to original rectangle and original rectangle has length L and width W. Need to know equation that represents relationship between L and W.

Okay; I think the exercise statement must be something along the lines of the following:

A Golden Rectangle has as its length L and width W sides which are in the following ratio:

\(\displaystyle \dfrac{L}{W} \, =\, \dfrac{\sqrt{5\,}\, +\, 1}{2}\)

It is known that, should one remove a square having all sides of length W from a Golden Rectangle, the remaining rectangle will be another Golden Rectangle.

Find an equation expressing the side lengths of this new, smaller, Golden Rectangle, in terms of the variables for the original rectangle.

Is this what you mean?

 

[Mas]

Golden rectangle

Yes.thank you sooooo much!

 

[stapel]

Yes.thank you sooooo much!

Okay, so now we have the text of the exercise. What have you tried in obtaining a solution?

Please be complete. Thank you.