Question

The height of a rectengular box is 4 times the width & the length is 3 inches more than the width. the volume of the box is 97. what is the width of the box?

Answer 1

let height, width, length be x,y,z respectively

Answer 2

x= 4y -- eqn 1
z=3+y -- eqn 2
xyz= 97 -- eqn 3

Answer 3

question reduce to 4x^3 +12x^2-97=0 where x is the width

Answer 4

\[\text{width}=\frac{1}{12} \left(-12+\left(19224-1944 \sqrt{97}\right)^{1/3}+6 \left(89+9 \sqrt{97}\right)^{1/3}\right)\text{ inches} \]or 2.16650 inches to 6 digits