Question

The volume, in cubic inches, of a retangular box can be expressed as the product of its three dimensions and with the given function V(x). The length is (x+3).

a) Find the linear expressions for the other dimensions. Assume that the width is greater than the height.
b) If x = 4, what are the dimensions of the rectangle?
c) What is the volume of the rectangle?

Answer 1

To find the linear expressions for the other dimensions of the rectangular box, assign variables to the width and height. When x = 4, the dimensions of the rectangle are length = 7 inches, width = 6 inches, and height = 4 inches. The volume of the rectangle is 168 cubic inches.

Step-by-step explanation:

Linear Expressions for the Other Dimensions:

To find the linear expressions for the other dimensions, we need to use the given information. The length of the rectangular box is (x+3). Let's assign variables to the other two dimensions. Let the width be (x+2), and the height be x.

Dimensions of the Rectangle (when x = 4):

To find the dimensions of the rectangle when x = 4, substitute x = 4 into the linear expressions for the dimensions. The length is (4+3) = 7 inches, the width is (4+2) = 6 inches, and the height is 4 inches.

Volume of the Rectangle:

The volume of a rectangular box is the product of its three dimensions. Substitute the dimensions into the volume function, V(x), to find the volume of the rectangle. When x = 4, the volume is (7 * 6 * 4) = 168 cubic inches.