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).