Let's go through each part step by step, completing the expressions as needed.
Part 1
(a) Height of the box:
When you cut squares of side length \( x \) from each corner and fold up the sides, the height of the box will be equal to the side length of the squares cut out. Thus, the height of the box is:
The height of the box is \( x \) inches.
Part 2
(b) Dimensions of the base of the box:
When you cut a square of side length \( x \) from each corner of the original piece of tin (which has dimensions 28 inches by 28 inches), the length and width of the base of the box will be reduced by \( 2x \) (since \( x \) is cut from both sides).
Therefore, the dimensions of the base of the constructed box are:
- Length: \( 28 - 2x \) inches
- Width: \( 28 - 2x \) inches
So, the dimensions of the base of the box are:
The dimensions of the base of the constructed box are \( 28 - 2x \) inches by \( 28 - 2x \) inches.
Let's recapitulate:
- Height: \( x \) inches
- Base dimensions: \( (28 - 2x) \) inches by \( (28 - 2x) \) inches
If you need help with parts (c), (d), or (e), please let me know!