The "Golden Rectangle" is a rectangle that has the following ratio of width to heigth. If the width 11, what is the height?

Question

11/h + h/11+h 

Answer 1

For a Golden Rectangle:

 

length : width :: 1.618 : 1

length : 11 : 1.618 : 1            product of means/extremes

length = 11(1.618)

length = 17.798

 

This is an approximation (but then if you are measuring what else would you need?).

 

For an exact value (using √5),  substitute  (1+√5)/2 for 1.618.

Answer 2

Sorry, what you wrote is not a ratio.  The ratio of longer side of the golden rectangle to its shorter side is (1+√5)/2 which is approx. 1.618.  This is sometimes called the golden ratio.

 

(The ratio of shorter to longer is the reciprocal, which happens to be 0.618...

 

You can set the ratio as x / 11 = (1+√5)/2 and solve for x, the longer side.

 

You can see lots of info on this topic by Googling it.