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The problem in the image describes creating a box from a rectangular piece of cardboard by cutting out squares from the corners. Let's break it down and write the necessary expressions.

### Given:
- The original rectangular cardboard is **18 inches long** and **12 inches wide**.
- **Squares of side length "x" inches** are cut from each corner.
- The sides are bent upwards to form a box.

### a. Write expressions for the length, width, and height of the box:
1. **Length of the box**: 
   The original length of the cardboard is 18 inches. After cutting out squares of side length \(x\) from each corner, the remaining length is:
   \[
   \text{Length} = 18 - 2x
   \]
2. **Width of the box**: 
   The original width of the cardboard is 12 inches. After cutting out squares of side length \(x\) from each corner, the remaining width is:
   \[
   \text{Width} = 12 - 2x
   \]
3. **Height of the box**: 
   Since squares of side length \(x\) are cut out, when the sides are bent upwards, the height of the box is simply:
   \[
   \text{Height} = x
   \]

### Final Expressions:
- Length = \(18 - 2x\)
- Width = \(12 - 2x\)
- Height = \(x\)

Let me know if you have any questions or want further clarification on any part of this problem!

Here are 5 related questions for practice:
1. What is the volume of the box in terms of \(x\)?
2. What is the maximum possible height \(x\) for the box?
3. How would the box dimensions change if the original cardboard was square?
4. If \(x = 2\), what are the final dimensions of the box?
5. What would the area of the base of the box be after cutting out the squares?

### Tip: 
Always verify that the value of \(x\) chosen makes sense in terms of the original dimensions of the cardboard (i.e., \(x\) must be smaller than half the width or length).

A box is to be made out of a rectangular piece of cardboard that is 12 inches wide and 18 inches long. Squares x inches on a side are cut out of the corners, and the sides are bent upwards. Write expressions for the length, width, and height of the box.

This problem involves creating a box by cutting squares from the corners of a rectangular piece of cardboard. It covers concepts such as algebraic expressions for dimensions (length, width, height), with the original cardboard being 18 inches long and 12 inches wide.

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