A box can be formed by cutting squares out of each corner of a piece of tin and folding the​ "tabs" up. Suppose the piece of tin is 28 inches by 28 inches and each side of the square that is cut out has length x.

Question

Complete parts ​(a) through ​(e).
28
28
28
28
x
x
Question content area bottom
Part 1
​(a) Write an expression for the height of the box that is constructed.
The height of the box is
  
x inches.
Part 2
​(b) Write an expression for the dimensions of the base of the box that is constructed.
The dimensions of the base of the constructed box are
  
28 inches by
  
28 inches.

Answer 1

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!