Answer:
The dimensions are height=4 inches, width=8 inches and lenght=12 inches.
Step-by-step explanation:
The volumen of a box is:
[tex]V=(height*lenght*width)\\[/tex]
we don't know the width so let's assume it as x.
[tex]V=4*x*(x+4)\\[/tex]
that gives us a cuadratic equation:
[tex]4x^{2} +16x=384[/tex]
let's rerrangage it:
∞[tex]4x^{2} +16x-384=0[/tex]
we can obtain the value of x using the quadratic formula:
[tex]\frac{-b^2\±\sqrt{b^2-4a*c} }{2a}[/tex]
that formula gave us two results:
[tex]x=8\\x=-12[/tex]
we have to take te possitive number, so the width is 8 inches and the length is 8+4=12 inches
height=4 inches
width=8 inches
lenght=12 inches
Volume=4*8*12=384 cubic inches.
