Answer:
width = 5 in
length = 5+4=9 in
height = 2(5)= 10 in
Step-by-step explanation:
A gift box has a volume of 450 cubic inches.
Let 'w' be the width of the box
The width of the box is 4 inches less than the length.
[tex]length = w+4[/tex]
The height is twice the width.
[tex]height = 2 \cdot width[/tex]
height = 2w
Volume of box = length times width times height
[tex]V=(w+4)(w)(2w)[/tex]
[tex]450=(w+4)(w)(2w)[/tex]
[tex]450=2w^3+8w^2[/tex]
[tex]2w^3+8w^2-450=0[/tex]
[tex]\quad 2\left(w-5\right)\left(w^2+9w+45\right)=0[/tex]
[tex]w-5=0[/tex]
w=5
[tex]\quad\left(w^2+9w+45\right)=0[/tex], this gives two complex values
so width = 5
length = 5+4=9
height = 2(5)= 10
