如果正方形的边是 10 厘米，那么如果边长加倍，新的周长将是多少倍？

正方形是一个有四个边和四个角的封闭二维图形。所有四个边的长度相等且彼此平行。正方形的基本图形如下所示。

正方形是四边形，其中：

• 对边是平行的。
• 四边相等。
• 所有角度均为 90°。

正方形的周长

正方形边界的长度可以通过对其所有边进行求和来计算，由下式给出，

正方形的周长=边+边+边+边。

因此，正方形的周长 = (4 × Side) 单位

如果正方形的边是 10 厘米，那么如果边长加倍，新的周长将是多少倍？

解决方案：

Here we will be finding how many times the perimeter of a square will be changed if we double the sides of the square

Perimeter of a square = Side + Side + Side + Side

Perimeter of a square = 4 × Side

Here we have the side of the square = 10 cm

Putting the value of the side of square in the perimeter of a square formula

Perimeter of a square = 4 × 10

Perimeter of a square = 40 cm  ………….(1)

When the side of the square is doubled 

The side of the new square becomes 2 × 10 cm = 20 cm

Perimeter of the new square = 4 × Side

Perimeter of the new square = 4 × 20

Perimeter of the new square = 80 cm  ……….(2)

Now we will be finding the change in the perimeter after increasing the side of the square

Perimeter of the original square = 40 cm  (from 1)

Perimeter of the new square = 80 cm  (from 2)

To find the increase in the perimeter

Subtract (1) from (2)

Increase in Perimeter = Perimeter of the new square – Perimeter of the original square 

⇒ Increase in Perimeter = 80 – 40 

⇒ Increase in Perimeter = 40 cm

To find how many times the perimeter is increased

Increase in the perimeter = $\frac{Perimeter\ of\ the\ new\ square}{Perimeter\ of\ the\ original\ square}$

Increase in the perimeter = $\frac{80}{40}$

Increase in the perimeter = 2 times

Therefore,

We can see that the perimeter of the new square is double the perimeter of the original square

Thus,

The perimeter of a square is increased by 2 times when its sides are doubled.

类似问题

问题 1. 如果正方形的边是 20 厘米，它的边是三倍，求新的周长增加了多少倍？

解决方案：

Here we have to find how many times the perimeter will be increased if the side of the square is tripled

As we know that

Perimeter of a square = 4 × side

Given : Side of the square is 20 cm

Perimeter of a square = 4 × 20

Perimeter of a square = 80 cm

Further,

When the side of the square is tripled

Side of the new square = 3 × 20

Side of the new square = 60 cm

Now,

Perimeter of the new square = 4 × side

Perimeter of the new square = 4 × 60

Perimeter of the new square = 240 cm

Further we will find the increase in perimeter

Increase in Perimeter = Perimeter of the new square – Perimeter of the original square 

Increase in Perimeter = 240 – 80

Increase in Perimeter = 160

To find how many times the perimeter is increased

Increase in the perimeter = $\frac{Perimeter\ of\ the\ new\ square}{Perimeter\ of\ the\ original\ square}$

Increase in the perimeter = $\frac{240}{80}$

Increase in the perimeter = 3 times

Therefore,

We can see that the perimeter of the new square is triple the perimeter of the original square

Thus,

The perimeter of a square is increased by 3 times when its sides are tripled.

问题 2. 如果正方形的边减少一半，求正方形的周长会减少多少倍。原来正方形的边是50厘米？

解决方案：

Here we have to find how many times the perimeter will be reduced if the side of the square is halved.

As we know that

Perimeter of a square = 4 × side

Given: Side of the square is 50 cm

Perimeter of a square = 4 × 50

Perimeter of a square = 200 cm

Further,

When the side of the square is halved

Side of the new square = $\frac{1}{2}\times50$

Side of the new square = 25 cm

Now,

Perimeter of the new square = 4 × side

Perimeter of the new square = 4 × 25

Perimeter of the new square = 100 cm

Further we will find the decrease in perimeter

Increase in Perimeter = Perimeter of the original square – Perimeter of the new square

Decrease in Perimeter = 200 – 100

Decrease in Perimeter = 100 cm

To find how many times the perimeter is decreased 

 in the perimeter = $\frac{Perimeter\ of\ the\ original\ square}{Perimeter\ of\ the\ new\ square}$

Decrease in the perimeter = $\frac{200}{100}$

Decrease in the perimeter = 2 times

Therefore,

We can see that the perimeter of the new square is reduced by 2 times the perimeter of the original square

Thus,

The perimeter of a square is reduced to half when its sides are halved.

问题 3. 如果正方形的周长增加了四倍，那么求新正方形的边增加了多少倍。原正方形的周长是160厘米？

解决方案：

Here we have to find the increase in the side of the square when its perimeter is increased by four times

As we know that

Perimeter of a square = 4 × side

Given: Perimeter of the original square is 160 cm

Perimeter of the original square = 160 cm

Perimeter of the original square = 4 × side

160 = 4 × side

Side = $\frac{160}{4}$

Side of the original square = 40 cm

Further,

Perimeter of the original square is increased by four times

Perimeter of the new square = 4 × 160

Perimeter of the new square = 640 cm

Perimeter of the new square = 4 × side

640 = 4 × side

Side = $\frac{640}{4}$

Side = 160 cm

Side of the new square = 160 cm

Now,

Side of the original square = 40 cm

Side of the new square = 160 cm

Increase in side = Side of the new square – Side of the original square 

Increase in Perimeter = 160 – 40

Increase in Perimeter = 120 cm

To find how many times the side is increased

Increase in the side = $\frac{Side\ of\ the\ new\ square}{Side\ of\ the\ original\ square}$

Increase in the perimeter = $\frac{160}{40}$

Increase in the perimeter = 4 times

Therefore,

We can see that the side of the new square is increased by four times the side of the original square

Thus,

The side of a square is increased by four times when its perimeter is increased by four times.

问题 4. 求正方形的周长是它的面积是 25 cm ²吗？

解决方案：

Here we have to find the perimeter of the square by the given area.

Given: Area of the square is 25 cm².

As we know that

Area of the square = Side × Side

25 = s × s

s² = 25

s = $\sqrt{25}$

s = 5 cm

Side of the square is 5 cm

Further,

Perimeter of the square = 4 × side

Perimeter of the square = 4 × 5

Perimeter of the square = 20 cm

Therefore,

Perimeter of the square is 20 cm if its area is 25 cm².

问题 5. 如果正方形的边增加 2 倍，则求新正方形的面积是多少倍。原正方形的边长为 10 厘米。

解决方案：

Here we have to find how many times the area will be increased if the side of the square is doubled

As we know that

Area of a square = side × side

Given: Side of the square is 10 cm

Area of a square = 10 × 10

Area of a square = 100 cm²

Further,

When the side of the square is doubled

Side of the new square = 2 × 10

Side of the new square = 20 cm

Now,

Area of the new square = side × side

Area of the new square = 20 × 20

Perimeter of the new square = 400 cm²

Further we will find the increase in area

Increase in area = Area of the new square – Area of the original square

Increase in Area = 400 – 100

Increase in Area = 300

To find how many times the area is increased

Increase in the area = $\frac{Area\ of\ the\ new\ square}{Area\ of\ the\ original\ square}$

Increase in the area = $\frac{400}{100}$

Increase in the area = 4 times

Therefore,

We can see that the area of the new square is 4 times the area of the original square

Thus,

The area of a square is increased by 4 times when its sides are doubled.