The Vsum of the Perimeters of an Equilateral Triangle and a Square

Multiple Choice

The vsum of the perimeters of an equilateral triangle and a square is 19. Find the dimensions of the triangle and the square that produce a minimum total area.

A) side of square: $\frac { 19 } { 4 + 9 \sqrt { 3 } }$ ; side of triangle: $\frac { 57 \sqrt { 3 } } { 4 + 9 \sqrt { 3 } }$
B) side of square: $\frac { 19 \sqrt { 3 } } { 9 + 4 \sqrt { 3 } }$ ; side of triangle: $\frac { 57 } { 9 + 4 \sqrt { 3 } }$
C) side of square: $\frac { 57 \sqrt { 3 } } { 4 + 9 \sqrt { 3 } }$ ; side of triangle: $\frac { 19 } { 4 + 9 \sqrt { 3 } }$
D) side of square: $\frac { 19 } { 9 + 4 \sqrt { 3 } }$ ; side of triangle: $\frac { 38 \sqrt { 3 } } { 9 + 4 \sqrt { 3 } }$
E) side of square: $\frac { 57 } { 9 + 4 \sqrt { 3 } }$ ; side of triangle: $\frac { 19 } { 9 + 4 \sqrt { 3 } }$