Question

The volume of a box is 384 cubic inches. the hieght of the box is 4 inches and the length of the box is 4 inches longer than its width. What are the dimensions of the box?

Answer 1

The dimensions are height=4 inches, width=8 inches and lenght=12 inches.

Explanation:

The volumen of a box is:

`V=(height*lenght*width)\\`

we don't know the width so let's assume it as x.

`V=4*x*(x+4)\\`

that gives us a cuadratic equation:

`4x^(2) +16x=384`

let's rerrangage it:

∞
`4x^(2) +16x-384=0`

we can obtain the value of x using the quadratic formula:

`(-b^2\±√(b^2-4a*c) )/(2a)`

that formula gave us two results:

`x=8\\x=-12`

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.