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A boiler room has the shape of a rectangular prism. The area of the floor of the room is 112 square feet. The length of the room is 2 feet more than twice the width. The height is 1 foot greater than the width.
What is the volume of the room in cubic feet?

Answer :

Answer:

The volume of room is 784 cubic feet.

Step-by-step explanation:

We are given the following in the question:

Area of floor = 112 square feet

Let w be the width, l be the length and h be the height of the room.

Then, according to the given information:

[tex]l = 2w+2\\h = 1+w[/tex]

Area of room:

[tex]A =\text{length}\times \text{width}\\112 = (2w+2)w\\112=2w^2+2w\\2w^2+2w-112=0\\w^2+2-56=0\\(w+8)(w-7)=0\\w=-8,7[/tex]

Since the width cannot be negative, the width of the room is 7 feet.

[tex]l = 2w+2=16\text{ feet}\\h = 1+w=8\text{ feet}[/tex]

Volume =

[tex]V=l\times w\times h\\V =14\times 7\times 8\\V=784\text{ cubic feet}[/tex]

Thus, the volume of room is 784 cubic feet.

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