The storage space in a moving truck is shaped like a rectangular prism. It has a total volume of 16 cubic meters. The height and width are both 2 meters less than the depth. What are the dimensions of the storage space?​

The dimensions are four by two by two meters.

Step-by-step explanation:

The volume for a rectangular prism is given by:

Where l is the length (or depth), w is the width, and h is the height.

Since the height and width are both two meters less than the depth, we can write that:

We are also given that the total volume is 16 cubic meters. Substitute:

Expand:

Distribute:

Isolate the equation. So:

We can factor by grouping. From the first two terms, factor out a l² and from the last two terms, factor out a 4:

Factor:

Zero Product Property:

Solve for each case:

Since we cannot take the square root of a negative number, we can ignore the first case.

Therefore, the length (or depth) of the storage space is four meters.

Thus, the dimensions are four by two by two meters.

the solution is 12x-6y