Explain why it is possible to draw more than two different rectangles with an area of 36 square units, but it is not possible to draw more than two different rectangles with an area of 15 square units. The sides of the rectangles are whole numbers. EXPLAIN your answer.

THX

factor pairs of 36:

1 36
2 18
3 12
4 9 ---- so I could draw 4 different rectangles of area 36 with whole number sides

factor pairs of 15
1 15
3 5 ---> only 2 possible

Use the grid to draw three different rectangles so that each has an area of 12 square units and they all have different widths. What are the dimensions of the rectangles.

alice wants to find all the prime factors of the number you get when you multiply 17times 11 times 13 times . she thinks she has to use a calulator to perform all thr multiplication and then find the prime factorization of the resulting number.do you agree?why or why not?

Because 36 has more factors than 15

To understand why it is possible to draw more than two different rectangles with an area of 36 square units but not with an area of 15 square units, we need to consider the factors of each number.

First, let's look at the factors of 36. Factors are the numbers that can divide a given number without leaving a remainder.

The factors of 36 are:
1, 2, 3, 4, 6, 9, 12, 18, 36

Now, let's try to form rectangles using these factors as the length and width. Since the sides of the rectangles need to be whole numbers, we can pair up the factors:

(1 × 36), (2 × 18), (3 × 12), (4 × 9), (6 × 6)

By pairing up these factors, we can create five different rectangles with an area of 36 square units. Thus, it is possible to draw more than two different rectangles with an area of 36.

Now, let's examine the factors of 15:

The factors of 15 are:
1, 3, 5, 15

Notice that there are only four factors for 15. Since we need two different whole numbers as the length and width of the rectangle, we can only create two different rectangles with an area of 15 square units:

(1 × 15), (3 × 5)

Therefore, it is not possible to draw more than two different rectangles with an area of 15 square units because there are limited factors available.

In conclusion, the number of factors a given number has determines the number of different rectangles we can form with that area. In the case of 36, which has nine factors, we can create five different rectangles, whereas in the case of 15, which has only four factors, we can create only two different rectangles.