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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.


Sagot :

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!

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