golden rectangle check

[Obsession]

I have an interesting rectangle here. If I cut a square off it, the remaining rectangle is similar to the original one (same shape, different size).

If the width of my rectangle is one meter, what is its length?

Only exact answers will be accepted (which means that since the answer is irrational, a decimal number will not be correct).

Since the problem says that the smaller rectangle is similar to the
bigger one, we know that it's a ratio. But since many rectangles
don't have a constant ratio of the length to its width, we can
confirm that Larry's rectangle is a golden rectangle. Golden
rectangles have a ratio of 1.618 which is found from 1 + (sqrt)5 /
2. To find the unknown side you have to multiply the given side by
the golden ratio- 1.618.
We are told that the side 1 meter. So to find the other side we have
to multiply 1 by 1.618.
1 * 1.618
= 1.618.

So the length is 1.618 meters. Rounded off the length is about 2
meters. The length is also shown as 1 +(sqrt)5/2.

---
is this right?

 

[jacket81]

Ok, I could be wrong, but here's how I figured it.
Letting w be width of smaller rectangle, and L be lenght, then w/L = L/(w+L).
And since w+L=1, and w=L^2, then L^2+L=1.
Then you can just subtract 1 and use quadratic formula.

 

[steve_b]

To Obsession:

Be careful when you write fractions:

1+sqrt(5)/2 is different from (1+sqrt(5))/2

The Golden Ratio is the second one. The 2 divides both terms: the 1 and the sqrt(5), so you need parentheses.

Steve