This GRE quantitative comparison question tests your understanding of geometry and putting an algebraic structure to the question.

The perimeter of a square and a rectangle in feet are equal. The length of the rectangle is $1$ foot longer than the width.

$\begin{array}{c c c c c c c c c c c}

& & & & & & \underline{\textrm{Quantity A}} & & & & \underline{\textrm{Quantity B}} \\

& & & & & & & & & & \\

& & & & & & \textrm{Area of square} & & & & \textrm{Area of rectangle} \\

\end{array}$

- $\quad \textrm{Quantity A is greater.}$
- $\quad \textrm{Quantity B is greater.}$
- $\quad \textrm{The two quantities are equal.}$
- $\quad \textrm{The relationship cannot be determined from the information given.}$