A nurse at a school is having a poster contest. The nurse sayS the size of the rectangular poster must be 72 square inches. Each side of the poster has to measure in whole inches. What are all the possible sizes of the poster board the nurse can cut to have ready?

A = LW

72 =
6 * 12
8 * 9

find all pairs of factors of 72

72
= 1 x 72
= 2 x 36
= 3 x 24
= .... etc

count them up, but I would not count the duplicates such as
....
24 x 3
36 x 2
72 x 1

To determine all the possible sizes of the poster board, we need to find all the factor pairs of 72.

The factor pairs of 72 are:
1 × 72 = 72
2 × 36 = 72
3 × 24 = 72
4 × 18 = 72
6 × 12 = 72
8 × 9 = 72

So, the possible sizes of the poster board that the nurse can cut to have ready are:
1 inch × 72 inches
2 inches × 36 inches
3 inches × 24 inches
4 inches × 18 inches
6 inches × 12 inches
8 inches × 9 inches

To find all the possible sizes of the rectangular poster board, we need to determine the dimensions (length and width) that result in a total area of 72 square inches.

First, let's list all the factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.

Now, for each factor, we can pair it with its corresponding factor to find the dimensions of the poster board. For example, for the factor 2, the corresponding factor is 72 ÷ 2 = 36. So the dimensions of the poster board would be 2 inches by 36 inches.

Here are all the possible dimensions of the poster board:

1 inch by 72 inches
2 inches by 36 inches
3 inches by 24 inches
4 inches by 18 inches
6 inches by 12 inches
8 inches by 9 inches
9 inches by 8 inches
12 inches by 6 inches
18 inches by 4 inches
24 inches by 3 inches
36 inches by 2 inches
72 inches by 1 inch

These are all the possible sizes of the poster boards that the nurse can cut to have ready.