Question

The length of a rectangular box is 4 times its width, and its height is 6 ft more than its width. The volume of the box is 47 ft3.

find the width of the box. Round your answer to two decimal places.

Answer 1

1.27

Explanation:

When completing word problems, it's always important to first turn everything into an equation.

The volume of a rectangular box is:

`V=lhw`

Where l is the length, h is the height, and w is the width.

Which we can write down the equation:

`47 ft^3=(4w)(6+w)(w)`

Next up, distribute:

`47=4w^2(6+w)\\47=24w^2+4w^3\\4w^3+24w^2-47=0`

We have a cubic equation, you can solve it using a calculator.

We have three solutions, and they are:

`w=-5.62919529..., -1.64201009..., 1.27120539...`

Since lengths cannot be negative, there is just one solution:
`w=1.27120539...`

And rounding it gives:

`w=1.27`

And don't forget to put ft at the end!