2006 Gauss 8 Problem 18

A square has perimeter 24. A rectangle has the same area as the square. If the width of the rectangle is 4, what is the perimeter of the rectangle?

\textbf{(A)}\ 26\quad \textbf{(B)}\ 36\quad \textbf{(C)}\ 16\quad \textbf{(D)}\ 32\quad \textbf{(E)}\ 24

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.