Question

The dimensions in inches of a shipping box can be expressed as width x, length x + 1, and height x - 4. The volume is 84 ft^3. Find the dimensions of the box in feet.

1, 1, 4
2, 2, 21
2, 6, 7
3, 4, 7

Please help? If somebody can help put this into an equation for me, I can do the rest. Thanks

Answer 1

84ft^3= (x-1)•x-4(x)

Maybe, then you would need to solve get the solution of x and plug it in for the demensions, hope this helps! (Not exactly positive that is my is correct but believe it is at least close!)

Answer 2

The dimensions of the box are

`2,6,7`

Explanation:

we know that

The volume of a box in the shape of a cube is equal to

`V=W*L*H`

where

W is the width of the box

L is the length of the box

H is the height of the box

In this problem we have

`V=84\ ft^(3)`

`W=x\ ft`

`L=x+1\ ft`

`H=x-4\ ft`

Substitute the values in the formula of volume

`84=x*(x+1)*(x-4)`

`84=(x^(2)+x)*(x-4)\\84=x^(3) -4x^(2)+x^(2)-4x\\84=x^(3)-3x^(2)-4x\\x^(3)-3x^(2)-4x-84=0`

Using a graphing tool

Solve the cubic function

see the attached figure

The value of x is equal to

`x=6\ ft`

the dimensions of the box are

`W=x\ ft=6\ ft`

`L=x+1\ ft=6+1=7\ ft`

`H=x-4\ ft=6-4=2\ ft`