How many different rectangles can be made into 24 squares with sides of 1 centimeter long?

There are four spellings, and the rectangular ones are: 24 cm long, 1 cm wide, 12 cm long, 2 cm wide, 3 cm long, 8 cm wide, 4 cm long, and 6 cm wide.

Problem solving ideas: fix the length of one side to see if the other side can meet the requirements, and transform the problem into a factor problem in mathematics for solution.

1. From the title, you can know that the side length of the square is one centimeter, that is, there will be no decimals, so you only need to consider the possibility of the integer range.

2. When one side of the fixed rectangle is 1 cm long, the other side is 24 cm. In the same way, when one side of the fixed rectangle is 2 cm long, then the other side is 24 cm, which meets the requirements; When one side of the fixed rectangle is 5 cm long, the other side does not meet the requirements. Here are all factors of 24; But "5" is not a factor of 40.

3. Through the above analysis, the problem can be transformed into a factor of 24, and how many combinations are there in which the product is 24? The results of this correspond to a rectangle of 24 cm in length, 1 cm in width, 12 cm in length, 2 cm in width, 3 cm in length, 8 cm in width, 4 cm in length, and 6 cm in width.

It can be spelled into four types, the length x width are:

1)24x1 (2)12x2 (3) 8x3 (4)6x4

Calculate it in his form. It shows that he has many methods, the screen is horizontal, vertical, all kinds, some are very long, and some are short. So the calculations are all different, read like this. So in my calculations, there are only 24 ways.

How many different rectangles can be made into 24 squares with sides of 1 centimeter long?

First, if you use it all, there are several ways to see 24 divisible:

1-1) 1*24, lined up.

1-2) 2*12, arranged in two rows, 12 in each row.

1-3) 3*8, arranged in three rows, 8 in each row.

1-4) 4*6, arranged in four rows, 6 in each row.

The rectangle is long and wide by default, so the solid one can only be placed in the above 4 types.

2. "Hollow" means a rectangular frame with 24 squares, rather than filling. This kind of circumference cannot be calculated as 24, but as 24 + 4 = 28, because the 4 small squares of the vertex will be double-counted when calculating the perimeter. This should be at least 3 rows.

2-1) (3 + 11) * 2 = 28, length 11 width 32-2) (4 + 10) * 2 = 28, length 10 width 42-3) (5 + 9) * 2 = 28, length 9 width 5

2-4) (6+8)*2=28, length 8 width 6

2-5) (7+7)*2=28, a large square with a side length of 7, a square is also a type of rectangle.

Therefore, 24 squares to a rectangle can spell 4 + 5 = 9 kinds.

Hope mine is helpful to you.

There are 4 kinds, the longest circumference in a row, and the shortest circumference of a 6 cm long and 4 cm wide rectangle.

The analysis process is as follows:

There are 4 ways to make a rectangle with 24 squares with a side length of 1 cm.

When the length and width of the rectangle are closer to each other, the girth is shorter, and when the length and width of the rectangle are not close, the girth is longer.

From this, it can be obtained: 24 = 24 1, the circumference is the longest at this time, and the arrangement at this time is lined up. The circumference is 2 (24+1) = 50 cm.

From this, it can be obtained: 24 = 6 4, the circumference is the shortest, and the arrangement at this time is arranged into a rectangle 6 cm long and 4 cm wide, with a circumference of 2 (6+4) = 20 cm.

There are 24 small squares with a side length of 1 cm, and the rectangles that can be put together are as follows: 1: 24 in a row, and the circumference is.

1+24)x2=50 cm;

2: 12 in a row, 2 in a row, the circumference is (2+12)x2=28 cm;

3: 8 in a row, 3 in a row, the circumference is (3+8)x2=22 cm;

4: 6 in a row, 4 in a row, the perimeter is.

4+6)x2=20 cm.

4 types of arrangement.

First of all, 28 is written as the form of multiplication of factors, that is, 28 = 1 28 = 2 14 = 4 7, there are only three forms of multiplication, so there are only three spellings: 28 cm long, 1 cm wide, 14 cm long, 2 cm wide, 7 cm long. Width 4 cm.

Arrange them horizontally in single rows one by one.

Every two grains in a row, arranged horizontally.

Each of the four grains is arranged in a row horizontally.

A single grain spells out a hollow rectangle.

Problem solving ideas: determine the length of one side to see if the other side can meet the requirements of the question stem, and calculate the transformation factor of the problem to facilitate understanding and solution.

1. As mentioned in the title, the side length of the square is one centimeter, that is, there will be no decimals, so only the whole range needs to be considered.

2. When determining that the length of the side of the long side is 1 cm, then the other side is 28 cm. In the same way, when it is determined that the side length of one side is 2 cm, the other side is 14 cm, which meets the requirements; When it is determined that one side is 3 cm long, the other side does not meet the requirements. The numbers in "1 cm", "28 cm", "2 cm" and "14 cm" are all factors of 40; But "3" is not a factor of 40.

3. By analogy, the problem can be transformed into a factor of 28 multiplied to get how many combinations of 28 can be obtained? In this way, the problem can be simplified, and the result is that 1 and 7 correspond to the various cases of the rectangle.

The first is 28 cm long and 1 cm wide.

The second is 14 cm long and 2 cm wide.

The third type is 7 cm long and 4 cm wide.

There are three spellings, which are shown as follows:

1. Spelling 1: The length of the new rectangle is zhi1 12 = 12 (cm); The width is 1 cm; The circumference is zhuan(12+1) 2=26 (cm).

2. Spelling 2: The length of the new rectangle is 1 6 = 6 (cm); The width is: 1 2 = 2 (cm); The circumference is (6+2) 2=16 (cm).

3. Spelling 3: The length of the new rectangle is 1 4 = 4 (cm); The width is: 1 3 = 3 (cm); The circumference is (4+3) 2=14 (cm).

A: The circumference of the new rectangle is 26 cm or 16 cm or 14 cm.

With 12 squares with a side length of 1 cm, you can spell out "3

rectangles of different shapes, of which the largest rectangle with the largest circumference is 26 centimeters long and 1 cm wide

centimeters, the area of the rectangle is 12

Cm.

According to the analysis, the area of the figure remains unchanged after spelling, and the length and width of the rectangle after spelling can be divided into the following situations:

1) 20 cm long, 1 cm wide, circumference is: (20 + 1) 2 = 42 (cm);

2) 10 cm long, 2 cm wide, and the circumference is: (10+2) 2=24 (cm);

3) 5 cm long, 4 cm wide, and the circumference is (4+5) 2=18 (cm);

A: There are 3 different spellings, with the largest circumference being 42 cm

Summary. There are four ways to put together a rectangle with 24 squares with sides of 1 centimeter.

So there are four ways to put together 24 squares with sides 1 cm long to form a rectangle.

How many different ways are there to make a rectangle out of 24 squares with sides of 1 centimeter? What is their circumference and area?

Hello, I have received your question, and I will be happy to answer your question.

Reply right away, wait a minute.

With 24 sides of the length of the cavity for the cavity of 1 centimeter of the square to form a rectangle, there are four empty circles of the line of spelling: 24 = 1 24 = 2 12 = 3 8 = 4 6 to 24 sides of the length of 1 centimeter of the square to form a rectangle, there are four spellings.

The area does not change equal to the 24 circumference changes, which are 50 cm, 28 cm, 22 cm, and 20 cm.