The Golden Rectangle

The Golden Rectangle: It is a rectangle whose sides are in ratio   and if we cut a square out of the current rectangle the rectangle left is similar to the actual rectangle.

Lets consider a rectangle with sides and

Lets cut a square of side out of the rectangle

The new rectangle will have side , as the two rectangles are similar to each other, we can write

 

 

Rearranging the above gives us 

 

Solving the above quadratic equation gives us two root, i.e. 

The positive root of the equation i.e. is known as the golden ratio.