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

Answer:

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

Step-by-step 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:

$\frac{-b^2\±\sqrt{b^2-4a*c} }{2a}$

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.