如果矩形的长度加倍而宽度保持不变，矩形的面积会发生什么变化？
在数学中，测量处理几何图形和体积、面积、形状、表面积等参数。或者换句话说，当我们处理面积、特定形状的体积或几何图形的不同参数时，它被称为数学测量。
长方形
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。一个矩形由两对平行的边组成，分别是长和宽。
矩形的属性
- 一个长方形有四个边和四个角。
- 矩形的角是直角，每个角都是 90°。
- 矩形的对边平行且长度相等。
- 矩形的对角线相互平分，两条对角线的长度相同。
- 一个长方形的所有内角之和等于360°。
矩形面积
一个矩形由相等的对组成，这些对在性质上平行且长度相等。矩形的面积是包围在其边界内的空间。或者换句话说，矩形的长度和宽度的乘积称为矩形的面积。
Area of rectangle = Length x Width
让我们假设 A 是矩形的面积，l 和 b 分别是矩形的长度和宽度。
A = l x b
如果矩形的长度加倍而宽度保持不变，矩形的面积会发生什么变化？
解决方案：
Let us assume A to be the original area of the rectangle.
Let us assume l and b to be the length and breadth of the original rectangle respectively.
Now,
A = l x b
Now,
Let us assume l’ and b’ to be the length and breadth of the new rectangle respectively.
A’ = l’ x b’
Now, the length is doubled and breadth remains the same, therefore,
l’ = 2l
b’ = b
We get,
A’ = 2l x b
A’ = 2 (l x b)
A’ = 2A
Hence, when the length is doubled and the breadth remaining the same then the area of the rectangle becomes twice
示例问题
问题一：长一倍宽宽减半时，矩形的面积如何变化？
解决方案：
We know,
Area of rectangle = length x breadth
Therefore,
A = l x b
Now,
l’ = 2l
b’ = b/2
Now, computing the area,
A’ = l’ x b’
A’ = 2l x b/2
A’ = l x b
Therefore, area remains same.
问题2：如果长度和宽度相等，面积如何变化？
解决方案：
We know,
Area of rectangle = length x breadth
Therefore,
Area of rectangle = length x length
= (length)2
In this situation, the rectangle becomes a square.
问题3：求长m倍宽n倍长方形面积变化的一般公式。
解决方案：
We know,
Area of rectangle, A = length x breadth
Therefore, in the modified case,
l ‘ = m x l
b’ = n x b
Area of rectangle, A’ = l’ x b’
Area of rectangle, A’ = m x l x n x b
Area of rectangle, A’ = m x n x (l x b)
A’ = m x n x A
Therefore, area becomes (m xn) times.
问题 4：使用上面的公式，定义如果长度变为 1/8 倍，宽度变为 2 倍，面积将如何变化。
解决方案：
Area of rectangle = length x breadth
A’ = 1/8 x 2 A
= 1/4 A
Therefore, the area becomes one-fourth times of the original area.
问题5：如果面积变成三倍，保持长度不变，宽度如何变化？
解决方案：
Area = length x breadth
Area’ = 3 x Area
Now,
Length’ x Breadth’ = 3 x Length x Breadth
Given, length is constant, length’ = length
Therefore,
Breadth’ = 3 x Breadth
Thus, breadth becomes three times.