What is the product of 6 and one-half and 9 and one-fourth? 15 and three-fourths

Data:
lenght=2x
width=x
height=y≥3

Volume=lenght x width x heigth
Therefore:
(2x)(x)(y)=38.72
2x²y=38.72

Area of the base: lenght x width
Area of the base=(2x)(x)=2x²
Cost of the base=12(2x²)=24x²

Area of the sides=2(length x height) + 2(width x height)
Area of the sides=2(2xy)+2(xy)=4xy+2xy=6xy
Cost of the sides=8(6xy)=48xy

Therefore:
Cost of the base + cost of the sides=538.56
24x²+48xy=538.56

We have this system of equations:
2x²y=38.72
24x²+48xy=538.56

We can solve this system of equations by substitution method:
2x²y=38.72    ⇒y=38.72 / 2x²=19.36 /x²

24x²+48x(19.36 / x²)=538.56
24x²+929.28/x=538.56
24x³+929.28=538.56x

I have solved this equation graphycally (by fooPlot) and the result would be:
x≈3.237  This value is not correct , because "y" would be < 3ft
And
x≈2.2   This value is correct, if "y" is at least 3 ft high.
Therefore:
width=x=2.2
lenght=2x=2(2.2)=4.4
y=19.36 / x²=19.36 / (2.2)²=4

it´s dimensions would be:
width=2.2 ft
lenght=4.4 ft
height=4 ft