Golden rectangle

A golden rectangle is a rectangle which ratio of length over width is equal to the Golden Mean.
Demonstrate that the rectangle ABCD is a golden rectangler.

In the triangle ABI right-angled at ,
based on the Pythagorean theorem:

BI²=    

BI =  
AD =
( +

 )  

AD

AB

=
  +  


 

construction of a golden rectangle