如果正方形的边是双倍的，那么求它的周长
正方形是由四个相等的边组成的几何图形。它是一个规则的四边形，其中所有的角度都是直角。基本上，它可以被认为是矩形的一种特殊情况，其中所有边的长度都相等。例如，一个方形的庭院。
正方形的性质
- 正方形的四个边相等。
- 正方形的对角线相等。
- 正方形的四个角都相等。
- 正方形的对角线平分它的角。
正方形的周长
正方形的周长称为包围几何图形的边界的总长度。
Perimeter of square = Sum of all sides of a square
让我们假设 s 是正方形的边。
因为，我们知道，正方形的所有边都是相等的。
Perimeter of square = s + s + s + s
Perimeter of square = 4s ….. (I)
如果正方形的边是双倍的，那么求它的周长。
解决方案：
Now,
Let us assume P to be the perimeter of the square. Now, as proved above,
P = 4s, where s is the side of the square….I
According to the question,
The side of the square is doubled.
Let us assume s’ to be the side of the new square and P’ to be its new perimeter.
Therefore,
s’ = 2s
We know,
P’ = 4s’
P’ = 4 x (2s)
P’ = 8s
Thus,
Perimeter becomes 8 times the original perimeter.
示例问题
问题 1. 如果正方形的周长是 28 厘米，请计算它的边需要增加多少才能使其周长翻倍？
解决方案：
Here we have to find the sides of the square to be increased to make its perimeter double.
Given:
Perimeter of square is 28 cm
As we know that
Perimeter of square = 4 x side (s)
28 = 4 x s
s = 28/4
s = 7 cm
When the perimeter of square is doubled
2 x perimeter of square = 2 x 28 = 56 cm
Further finding how much times the side has to be increased
As we know that
Perimeter of square = 4 x side (s’)
56 = 4 x s’
s’ = 56/4
s’ = 14 cm
Now,
How much times the side of the square has to be increased to make its perimeter double
= s’/s
= 14/7
= 2 times
Therefore,
The side of the square has to be increased twice in order to make its perimeter double.
问题 2. 推导正方形边长增加 n 倍时的通式。
解决方案：
Since, perimeter of a square is equivalent to 4 x side.
Originally,
P = 4 x s
Now, side is made n times.
Therefore,
s’ = n x s
New perimeter, P’ = 4 x s’
= 4 x n x s
= n P
问题 3. 使用上面的公式，求正方形边长为 1/3 时的周长。
解决方案：
Using the above-derived formula,
P’ = n P
Therefore,
Perimeter of the square becomes 1/3 times.
问题 4：如果正方形的两条边只有双倍，正方形的周长会怎样？
解决方案：
Since,
Perimeter is given by, P = s + s + s + s
Since, two sides are doubled, we have,
P’ = s + s + 2s + 2s
P’ = 2s + 2s + 2s
P’ = 6s