Congruent squares of length x are cut from the corners of an 8 inch by 12 inch piece of cardboard to create a box without a lid What is the... -Height of the box -Length of the box -Width of the box Write the function v(x) for the volumn of the box in terms of x. Leave in factored form.

1. The height if the box is x.

2. The length of the box is 8 - 2x

3. The width of the box is 12 - 2x

4. The volume of the box is   4x(6 - x)(4 - x)

Step-by-step explanation:

1. Since the squares of length x are cut from the corners of the cardboard, the height of the box is the length of a square which is x.

2. Since we have 8 inch by 12 inch, its length is 8 inches and its width 12 inches.

Since squares of x length are cut from the corners of the cardboard, the length of the box is 8 - 2x

3. Since we have 8 inch by 12 inch, its length is 8 inches and its width 12 inches.

Since squares of x length are cut from the corners of the cardboard, the width of the box is 12 - 2x

4. The volume of the box is V(x) = length × width × height = (12 - 2x)(8 - 2x)x = 2 × 2x(6 - x)(4 - x) =  4x(6 - x)(4 - x)