the width of the box is 1.21 ft
Explanation:
length of the box = 2 times the width
let the width = w
length = 2(w) = 2w
height = 6ft more than its width
height = 6ft + w = 6 + w
Volume of the rectangular box = length × width × height
Volume of the rectangular box = 2w × w × (6 + w)
Volume of the box is given as = 21ft³
21 = 2w × w × (6 + w)
21 = 2w²(6 + w)
21 = 12w² + 2w³
[tex]\begin{gathered} 2w^3+12w^2\text{ - 21 = 0} \\ U\sin g\text{ cubic formula:} \\ \text{values of w =}-5.673836,-1.53319,1.207026 \end{gathered}[/tex]
But since we can't have width as a negative number, w will be the positive number
w = 1.207206
[tex]\begin{gathered} To\text{ check:} \\ \text{volume = 2(}1.207206)\text{ }\times\text{ }1.207206\text{ }\times\text{ (6 + }1.207206) \\ \text{volume = 20.999 }\approx\text{ 21} \end{gathered}[/tex]
To two decimal place, w = 1.21
Hence, the width of the box is 1.21 ft
