Find x representing the length of a rectangle side

Question

A square with sides of length 1 is removed from the end of a rectangle with width 1 and length x. If the resulting rectangle is similar to the original rectangle, find x. The equation found from the proportion can be solved using the quadratic formula and only 1 possible solution exists. I got x^2 -x-1 which doesn't work. Please help!

Answer 1

You have the right equation.  You just have to realize that if you are going to remove a square with sides of length 1 from a rectangle with width 1 and length x, then x has to be greater than 1.  So any solution you get that is less than 1 is not valid for this problem.