A rectangular swimming pool is being designed with an area of $150{\text{ m}}^2$. Surrounding the pool on all sides is a uniform $2\text{ m}$ wide deck. What are the dimensions of the pool that minimize the total area (including the deck)?

$7\sqrt{6}\text{ m}\times 7\sqrt{5}\text{ m}$

$6\sqrt{6}\text{ m}\times 5\sqrt{5}\text{ m}$

$5\sqrt{6}\text{ m}\times 5\sqrt{6}\text{ m}$

$3\sqrt{15}\text{ m}\times 3\sqrt{15}\text{ m}$