求一个周长为 40 厘米，底为 5 厘米的长方形的长度
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°。一个所有边相等的矩形相当于一个正方形。一个长方形由两对平行的边组成，分别是长和宽。
矩形的属性
- 它有四个边和四个角。
- 所有的角度都是直角。
- 对面平行且长度相等。
矩形的周长
矩形的周长是矩形所有边的边界的总和。它是矩形所有边长的总和。
Perimeter of rectangle = Sum of all sides of rectangle
让我们假设 l 是矩形的长度，b 是矩形的宽度。
矩形的周长 = 长 + 宽 + 长 + 宽
让我们假设 P 是矩形的周长。
P = l + b + l + b
P = 2l + 2b
P = 2(l+b)
求一个周长为 40 厘米，底为 5 厘米的长方形的长度
解决方案：
According to the problem statement, we have,
Perimeter of rectangle = Length + Breadth + Length + Breadth
Let us assume P to be the perimeter of the rectangle and l and b to be its length and breadth respectively.
Now,
Perimeter, P = 2 (l+b)
Substituting the values,
P = 40 cm
40 = 2(l+5)
20 = l+5
l = 15 cm
Therefore, Length of the rectangle is 15 cm.
示例问题
问题 1. 如果一个长方形的周长是 100 厘米，宽是 10 厘米，那么求它的长？
解决方案：
Here we have to find the length of the rectangle when its perimeter and breadth are given,
Given:
Perimeter of rectangle = 100 cm
Breadth of the rectangle = 10 cm
We have to find
Length of the rectangle = assume ‘l’
As we know that
Perimeter of rectangle = 2×(length + breadth)
Putting the given values in the formula
100 = 2×(l + 10)
100 = 2l + 20
100 – 20 = 2l
2l = 80
l = 80/2
l = 40 cm
Therefore,
Length of the rectangle is 40 cm.
问题 2. 矩形周长为 250 m，长度为 100 m，计算矩形公园的宽度？
解决方案：
Here we have to find the breadth of the rectangle when its perimeter and length are given,
Given:
Perimeter of rectangle = 250 m
Length of the rectangle = 100 m
We have to find
Breadth of the rectangle = assume ‘b’
As we know that
Perimeter of rectangle = 2×(length + breadth)
Putting the given values in the formula
250 = 2×(100 + b)
250 = 200 + 2b
250 – 200 = 2b
2b = 50
b = 50/2
b = 25 m
Therefore,
Breadth of the rectangle is 25 m.
问题 3. 如果一个长方形的周长是 500 厘米，它的长度是宽度的 4 倍，那么求它的长和宽？
解决方案：
Here we have to find the length and breadth of the rectangle
We are given that the length of the rectangle is 4 times the breadth
Assume,
Length of rectangle = l
Breadth of rectangle = b
As per the question
Length of rectangle = 4 times the breadth
Length of rectangle = 4 × b
Length of rectangle = 4b
As we know that
Perimeter of rectangle = 2×(length + breadth)
Perimeter of rectangle = 2×(l + b)
Perimeter of rectangle = 2×(4b + b)
Perimeter of rectangle = 2×(5b)
500 = 10b
b = 500/10
b = 50 cm
Breadth = 50 cm
As given in the question
Length is 4 times the breadth
Length = 4 × 50
Length = 200 cm
Therefore,
Length of rectangle is 200 cm and breadth of rectangle is 50 cm.
问题 4. 如果矩形的周长是 1600 m，宽度是长度的 1/3，请计算矩形的长和宽？
解决方案：
Here we have to find the length and breadth of the rectangle
We are given that the breadth of the rectangle is 1/3 times the length
Further we can say that length of a rectangle is 3 times its breadth
Assume,
Length of rectangle = l
Breadth of rectangle = b
Length of rectangle = 3 times the breadth
Length of rectangle = 3 × b
Length of rectangle = 3b
As we know that
Perimeter of rectangle = 2×(length + breadth)
Perimeter of rectangle = 2×(l + b)
Perimeter of rectangle = 2×(3b + b)
Perimeter of rectangle = 2×(4b)
1600 = 8b
b = 1600/8
b = 200 m
Breadth = 200 m
As given in the question
Length is 3 times the breadth
Length = 3 × 200
Length = 600 m
Therefore,
Length of rectangle is 600 m and breadth of rectangle is 200 m.