Question

1. a box is to be formed by cutting square pieces out of the corner of a rectangular piece of a 4\ by 6\ note card as shown below. the sides will then be folded up to make the box.

part i: (6 points)
a. what is the original length (long side) of the note card?
b. how many pieces of length x have been cut from the original length?
c. write the resulting length of the note card, once the pieces have been cut.
d. what is the original width (short side) of the note card?
e. how many pieces of length x have been cut from the original width?
f. write the resulting width of the note card once the pieces have been cut.

Explanation:

Step1: Identify original length

Given note - card is 4" by 6", so original length is 6".

Step2: Count pieces cut from length

2 pieces of length x are cut from the long - side (original length).

Step3: Calculate resulting length

Original length is 6", 2 pieces of length x are cut, so resulting length is $6 - 2x$.

Step4: Identify original width

Original width of the note - card is 4".

Step5: Count pieces cut from width

2 pieces of length x are cut from the short - side (original width).

Step6: Calculate resulting width

Original width is 4", 2 pieces of length x are cut, so resulting width is $4 - 2x$.

Answer:

A. 6"
B. 2
C. $6 - 2x$
D. 4"
E. 2
F. $4 - 2x$