如果每边的长度加倍，2平方英寸的周长是多少？

正方形是具有四个边的二维图形，最好分别表示为边，其交点分别称为顶点。正方形的所有四个边的长度都相等。这是所有边都相等的矩形的特殊情况

正方形的性质

正方形的一些属性如下：

• 正方形的所有四个边彼此相等。
• 正方形的对边相互平行。
• 正方形的所有角度都是 90°。
• 所有内角之和为360°。
• 对角线的长度相等。
• 边为 s 的对角线的长度为 √2 × s
• 由于正方形的边是平行的，所以它也被称为平行四边形。

正方形的周长

正方形的周长=所有四个边的总和

所以，

让我们假设正方形的边是x。

现在，

由于正方形的所有四个边的长度都相等，我们有，

正方形的周长 = x + x + x + x

= 4x

如果每边的长度加倍，2平方英寸的周长是多少？

解决方案：

Originally, we have,

Side of a square, s = 2 inch

Perimeter of the square, P = 4 * side of the square

= 4 * s inch

= 4 * 2 inch

= 8 inch

Thus, P = 8 inches

Now, we have,

Side of the square is doubled.

Therefore,

Side of a square, s’ = 2 * 2 inch

= 4 inch

Perimeter of the square, P’ = 4 * side of the square

= 4 * s’ inch

= 4 * 4 inch

= 16 inch

P’ = 16 inches

Thus, the perimeter becomes two times, when each side is doubled.

示例问题

问题 1. 假设正方形的边长是 40 英寸，如果正方形的边增加三倍，那么计算正方形的新周长是多少倍？

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 40 inch

Perimeter of a square = 4 × 40

Perimeter of a square = 160 inch

Further,

When the side of the square is tripled

Side of the new square = 3 × 40

Side of the new square = 120 inch

Now,

Perimeter of the new square = 4 × side

Perimeter of the new square = 4 × 120

Perimeter of the new square = 480 inch

Further, 

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 = $\frac{480}{160}$

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. 计算如果正方形的边减少到一半，正方形的周长将减少多少倍。鉴于原始正方形的边是 25 英寸？

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 25 inch

Perimeter of a square = 4 × 25

Perimeter of a square = 100 inch

Further,

When the side of the square is halved

Side of the new square = $\frac{1}{2}\times25$

Side of the new square = 12.5 inch

Now,

Perimeter of the new square = 4 × side

Perimeter of the new square = 4 × 12.5

Perimeter of the new square = 50 inch

To find how many times the perimeter is decreased

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

Decrease in the perimeter = $\frac{100}{50}$

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. 假设正方形的周长增加了四倍，那么求正方形的新边变成了多少倍。假设原正方形的周长是 120 英尺？

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 120 feet

Perimeter of the original square = 120 feet

Perimeter of the original square = 4 × side

120 = 4 × side

Side = $\frac{120}{4}$

Side of the original square = 30 feet

Further,

Perimeter of the original square is increased by four times

Perimeter of the new square = 4 × 120

Perimeter of the new square = 480 feet

Perimeter of the new square = 4 × side

480 = 4 × side

Side = $\frac{480}{4}$

Side = 120 feet

Side of the new square = 120 feet

Now,

Side of the original square = 30 feet

Side of the new square = 120 feet

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 = $\frac{120}{30}$

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. 如果正方形的面积是 64 英寸² ，请计算正方形的周长？

解决方案：

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

Given: Area of the square is 64 inch².

As we know that

Area of the square = Side × Side

Area of the square = s × s

64 = s × s

s² = 64

s = $\sqrt{64}$

s = 8 inch

Side of the square is 8 inch

Further,

Perimeter of the square = 4 × side

Perimeter of the square = 4 × 8

Perimeter of the square = 32 inch

Therefore,

Perimeter of the square is 32 inch.

问题5.假设正方形的边增加了8倍，那么计算新正方形的面积将变成多少倍。鉴于原始正方形的边是 20 英寸。

解决方案：

Here we have to find how many times the area will be increased if the side of the square is increased by 8 times.

As we know that

Area of a square = side × side

Given: Side of the square is 20 inch

Area of a square = 20 × 20

Area of a square = 400 inch²

Further,

When the side of the square is increased by 8 times

Side of the new square = 8 × 20

Side of the new square = 160 inch

Now,

Area of the new square = side × side

Area of the new square = 160 × 160

Perimeter of the new square = 25600 inch²

Further,

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 = $\frac{25600}{400}$

Increase in the area = 64 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 64 times when its sides are increased by 8 times.