Determine the Dimensions of a Rectangular Solid (With a Square $\frac { 20 \sqrt { 6 } } { 3 }$

Multiple Choice

Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 400 square meters.

A) square base side $\frac { 20 \sqrt { 6 } } { 3 }$ ; height $\frac { 20 \sqrt { 6 } } { 3 }$
B) square base side $\frac { 20 \sqrt { 6 } } { 3 }$ ; height $\frac { 10 \sqrt { 6 } } { 3 }$
C) square base side $\frac { 10 \sqrt { 6 } } { 3 }$ ; height $\frac { 20 \sqrt { 6 } } { 3 }$
D) square base side $\frac { 10 \sqrt { 6 } } { 3 }$ ; height $\frac { 10 \sqrt { 6 } } { 3 }$
E) square base side $\frac { 200 \sqrt { 6 } } { 3 }$ ; height $\frac { 10 \sqrt { 6 } } { 3 }$