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A high school Philanthropy Club is collecting plastic waste which will be used to create benches for a local park. The volume of the rectangular container, in cubic feet, used to hold the waste is modeled by the expression below, where x is the width of the container, in feet. If the length of the container is half of a foot longer than its width, what expression represents the height of the container?

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It is given that that length of the container is half of a foot longer than its width and that x is the width of the container. So, the length of the container can be represented by the expression below.

x+1/2

Recall that the formula for the volume of a rectangular prism is given by the formula V = l · w · h, where l is the length, w is the width, and h is the height.

Rewrite the given expression by factoring out the leading coefficient and x2. The expression left inside the parentheses should have a linear term with a leading coefficient of 1 to match the expression for the length of the container.

7x^3+3.5x^2

7x^2(x+1/2)

Now, rewrite this resulting expression as a product of three factors to represent the width, length, and height of the container.

7x^2(x+1/2)

7x*x*(x+1/2)

( * means multiply)

Thus, if the length of the container is half a foot longer than its width, x, then the expression 7x represents the height of the container.

Step-by-step explanation:

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