Answer:
1.27
Step-by-step explanation:
When completing word problems, it's always important to first turn everything into an equation.
The volume of a rectangular box is:
[tex]V=lhw[/tex]
Where l is the length, h is the height, and w is the width.
Which we can write down the equation:
[tex]47 ft^3=(4w)(6+w)(w)[/tex]
Next up, distribute:
[tex]47=4w^2(6+w)\\47=24w^2+4w^3\\4w^3+24w^2-47=0[/tex]
We have a cubic equation, you can solve it using a calculator.
We have three solutions, and they are:
[tex]w=-5.62919529..., -1.64201009..., 1.27120539...[/tex]
Since lengths cannot be negative, there is just one solution: [tex]w=1.27120539...[/tex]
And rounding it gives:
[tex]w=1.27[/tex]
And don't forget to put ft at the end!
