The goal is to find the height of the rectangular prism with the given information of its width and length. The volume of a rectangular prism is , where is width and is height.

Because we're given the final volume and two of the three variables, we can substitute in the information we know and solve for the missing variable.

Therefore, the height of the prism is .

When reading word problems, there are certain clues that help interpret what is going on. The word “is” generally means “=” and the word “times” means it will be multiplied by something. Therefore, “the length of a box is 3 times the width” gives you the answer: L = 3 x W, or L = 3W.

Since the length of the box is twice the width and the height is three times the width, and .

The surface area of the box is

To find the width:

Use the formula for finding the surface area of a right, rectangular prism,

and substitute the known values, and then solve for w.

So,

So, the width is 7 cm.

The formula for the volume of a right, rectangular prism is , so substitute the known values and solve for lenght.

. So the length is 8 inches.

The volume of a prism is length times width times height.

We are given the length is 7m and the width is 5m.

So, we plug these into our formula:

.

We then solve for height:

.

The height is therefore 6m.

If we let be the width of our prism, then since the length is twice the width, our length would be . Since the height is twice the length, our height would be .

Since the volume of a rectangular prism is simply the product of width, length, and height, we get

We then simply solve for the width.

Therefore, our width is 3. Since our length is twice the width, the length is 6.

We notice the width is “5 inches less than three times its width,” so we express W as being three times its width (3L) and 5 inches less than that is 3L minus 5. In this case, W is the dependent and L is the independent variable.

W = 3L - 5