Question 13807
dear friend 
let this be the figure
|------|----|
|------|----|1
|------|----|
|--1---|-x--|
     
so the length of the original rectangle is 1+x and breadth is 1
so the length of the new rectangle is 1 and breadth is x]

so     (1+x):1  =1:x
so     solving this we get (x^2)+x+1=0

solve it by the formula {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}   to get the ans