A carpenter is building a rectangular room with a fixed perimeter of $13$ ft $.$ What are the dimensions of the largest room that can be built? What is its area?

A$.6\mathrm{.}5$ by $6\mathrm{.}5$;$42\mathrm{.}25{}^2$

B$.1\mathrm{.}3$ by $11\mathrm{.}7$;$15\mathrm{.}21{}^2$

C$.3\mathrm{.}25$ by $9\mathrm{.}75$;$31\mathrm{.}6875{}^2$

D$.3\mathrm{.}25$ by $3\mathrm{.}25$;$10\mathrm{.}5625{}^2$