Answer:
[tex]64=(2x+6)(x+3)(x)[/tex]
is the required equation for volume of box.
Step-by-step explanation:
We are given the following in the question:
The box is [tex]x[/tex] inches wide.
Width, w =
[tex]x\text{ inches}[/tex]
Height of box, h =
[tex](x+3)\text{ inches}[/tex]
Length of box, l =
[tex]=2\times \text{Height of box}\\=2\times (x+3)\\=(2x+6)\text{ inches}[/tex]
Volume of box = 64 cubic inches
Formula:
[tex]V = l\times w\times h[/tex]
Putting values, we get,
[tex]V = (2x+6)(x+3)(x)\\64=(2x+6)(x+3)(x)\\64 = (2x+6)(x^2+3x)\\64 = 2x^3+6x^2+6x^2+18x)\\64 = 2x^3+12x^2+18x\\\Rightarrow 2x^3+12x^2+18x-64=0[/tex]
is the required equation.
