Question

The volume of a rectangular prism is represented by the function x3 + 11x2 + 20x – 32. The width of the box is x – 1 while the height is x + 8. Find the expression representing the length of the box

Answer 1

The length of the box is (x+4).

Explanation:

The volume of a rectangular prism is represented by the function

`f(x)=x^3+11x^2+20x-32`

Rewrite the given function in factored form.

`f(x)=(x-1)(x+8)(x+4)`

It is given that the width of the box is x – 1 while the height is x + 8.

The volume of a rectangular prism is

`V=l* b* h`

where, l is length, b is width and h is height.

Divide both sides by bh.

`(V)/(bh)=l`

Substitute the value of volume, height and width.

`((x-1)(x+8)(x+4))/((x-1)(x+8))=l`

Cancel out the common factors.

`(x+4)=l`

Therefore the length of the box is (x+4).

Answer 2

The volume of a rectangular prism is computed by a formula volume = length times width times height. So base on your given the volume is represented by x^3+11x^2+20-32 and the width is x-1 and height is x+8 the length is x+4 i hope i answered your question