Mathematics: 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

HINT: The sum of all three angles inside any triangle is 180°....

The volume of a rectangular prism is represented

mia3128

02.01.2022

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

Step-by-step 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

$V=l\times b\times h$

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

Divide both sides by bh.

$\frac{V}{bh}=l$

Substitute the value of volume, height and width.

$\frac{(x-1)(x+8)(x+4)}{(x-1)(x+8)}=l$

Cancel out the common factors.

(x+4)=l

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

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