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.

Length = 16 feet.

Width = 7 feet

Height = 8 feet

Volume = 896 cubic feet.

Step-by-step explanation:

There is a rectangular prism boiler room. 112 square feet is the floor area of the room.

Let the length of the room is L feet and width is W feet.

So, LW = 112 ... (1)

Now, given that L = 2 + 2W ... (2), hence, from equation (1) we get

(2 + 2W) W = 112

⇒ 2w + 2w² = 112

⇒ W² + W - 56 = 0

⇒ (W + 8) (W - 7) = 0

⇒ W = 7 feet. {Neglecting the negative root as W can not be negative}

Hence, from equation (2) we get L = 2W + 2 = 16 feet.

Now, 1 foot more than the width is the height H.

Hence, H = 7 + 1 = 8 feet.

Therefore, the volume of the room is, V = LWH = 16 * 7 * 8 = 896 cubic feet. (Answer)