周长为 24 厘米的矩形有多少个？

矩形是由四个边和四个顶点组成的封闭二维图形。矩形的所有角度都是 90 度。一个所有边相等的矩形相当于一个正方形。一个矩形由两对平行的边组成，分别是长和宽。

矩形的周长

矩形的周长是矩形外边界的长度。它也是通过矩形的长度和宽度的总测量值的总和来计算的。

矩形公式的周长

让我们假设一个周长为 P 的矩形，其长度和宽度分别为 'l' 和 'w' 为 2(l + w)。

Perimeter of a Rectangle Formula = 2 (Length + Width) units

周长为 24 厘米的矩形有多少个？

解决方案：

There may be multiple rectangles having a perimeter equivalent to 24 cm. For example, one rectangle of sides 5 cm and 7cm have perimeter 24, similarly, a rectangle of sides 4 cm and 8 cm have perimeter 24. So, there can be many rectangles of dimensions such as (5,7), (4,8), (3,9), (3.6,8.4), etc. 

If a and b are the sides of the rectangle then the perimeter is 2a+2b. You are given a string 24 cm long (which will be the perimeter) from which to make the rectangles. So,

2a + 2b = 24

2(a + b) = 24

a + b = 12

If the sides must be integers, then the possibilities are:

a = 1, b = 11

a = 2, b = 10

a = 3, b = 9

a = 4, b = 8

a = 5, b = 7

a = 6, b = 6

If a=7, then b=5 which is the same as the fifth rectangle listed, i.e., a=5, b=7.

So there are only 6 possible rectangles (the square a=6 & b=6, being a special case of a rectangle).

一步一步完成解决方案：

We know, 

The length of the string forming the rectangle is 24cm. Therefore, it can be concluded that the perimeter of the rectangle is equivalent to 24 cm.

The perimeter of a rectangle is given by 2(a+b)=P, which implies that the perimeter is equal to double of the sum of the sides of the rectangle. 

Substituting, we get, 

∴ 2(a+b) = 24

Therefore,

 (a+b) = 12

Starting with a = 6, b = 6.

On increasing the value by 1, we conclude that, following are the other sides of the rectangle

a = 7, b = 5

a = 8, b = 4

a = 9, b = 3

a = 10, b = 2

a = 11, b = 1

因此，我们只能说 6 个矩形是可能的，以下是这些矩形：

1. 6, 6, 6, 6
2. 5, 7, 5, 7
3. 4, 8, 4, 8
4. 3, 9, 3, 9
5. 2, 10, 2, 10
6. 1, 11, 1, 11

示例问题

问题 1. 假设长方形的边长为 6:4，周长为 100 厘米，求它的尺寸？

解决方案：

Here we have,

Perimeter of rectangle = 100 cm

Ratio of length and breadth is 6 : 4

We have to find length and breadth of the rectangle

Assume the common ratio be x

Thus, the sides will be 6x and 4x

As we know that,

Perimeter of the rectangle = 2(length + breadth)

Perimeter of the rectangle = 2(6x + 4x)

Perimeter of the rectangle = 2 × 10x

Perimeter of the rectangle = 20x

100 = 20x

x = 100/20

x = 5

Therefore,

Length = 6x = 6 × 5 = 30 cm

Breadth = 4x = 4 × 5 = 20 cm

Therefore, 

Length is 30 cm and breadth is 20 cm.

问题 2. 如果长方形的边长是 4:2，周长是 600 厘米，那么求它的尺寸？

解决方案：

Here we have,

Perimeter of rectangle = 600 m

Ratio of length and breadth is 4 : 2

We have to find length and breadth of the rectangle

Assume the common ratio be x

Thus, the sides will be 4x and 2x

As we know that,

Perimeter of the rectangle = 2(length + breadth)

Perimeter of the rectangle = 2(4x + 2x)

Perimeter of the rectangle = 2 × 6x

Perimeter of the rectangle = 12x

600 = 12x

x = 600/12

x = 50

Therefore,

Length = 4x = 4 × 50 = 200 m

Breadth = 2x = 2 × 50 = 100 m

Therefore,

Length is 200 m and breadth is 100 m.

问题 3. 找出长 1040 厘米、宽 280 厘米的长方形仓库地板需要多少块长 26 厘米、宽 14 厘米的瓷砖？

解决方案：

To find the number of tiles

First we need to find the area of tile and godown

Area of rectangle = Length × Breadth

Area of rectangle tile = 26 × 14

Area of rectangle tile = 364 cm²

Area of rectangle godown = 1040 × 280

Area of rectangle godown = 291200 cm²

Now,

Finding the number of tiles required

Number of tiles = Area of godown/ Area of a tile

Number of tiles = 291200/364

Number of tiles = 800 tiles

Therefore,

We will be needing 800 tiles to cover the godown floor.

问题 4. 以每米 20 卢比的费率计算面积为 3200 m ²的矩形操场的围栏成本？如果长度是宽度的两倍。

解决方案：

Here we have to find the cost of fencing the rectangular playground

As given in the question, length is double the breadth

Breadth = b

Length = 2 × b = 2b

First we need to find the length and breadth of the playground

Area of rectangle = Length × Breadth

Area of rectangular playground = 2b × b

3200 = 2b²

b² = 3200/2

b² = 1600

b = √1600

b = 40

Breadth = 40 m

Length = 2 × breadth = 2 × 40 = 80 m

Further,

Perimeter of the rectangle = 2(length + breadth)

Perimeter of the rectangle = 2(80 + 40)

Perimeter of the rectangle = 2 × 120

Perimeter of the rectangle = 240 m

Now,

Finding the cost of fencing

Cost of fencing the playground =   ₹20 × perimeter of the playground

Cost of fencing the playground =   ₹20 × 240

Cost of fencing the playground =   ₹480

Therefore,

Cost of fencing the rectangular playground is ₹480.