Question

Find the length of the suitcase.

Please help

Answer 1

The length of the suitcase is $x+4$ inches.

Step-by-step explanation:

Step 1:

The volume of a rectangular prism is obtained by multiplying its length, width, and height.

In the given diagram, the length is $l$ inches, the width is $(x+2)$ inches, and the height of the suitcase is $x$ inches.

The volume of the suitcase $= (length)(width)(height).$

The volume of the suitcase is given as $x^{3} + 6x^{2} +8x.$

Step 2:

By substituting the values in the equation, we get

$x^{3} + 6x^{2} +8x= (length)(width)(height).$

$x^{3} + 6x^{2} +8x= (l)(x+2)(x).$

$x^{3} + 6x^{2} +8x= (l)(x^{2}+2x).$

$l=\frac{x^{3} + 6x^{2} +8x}{x^{2}+2x}, l = x+4.$

So the length of the suitcase is $x+4$ inches.