一个男孩在一个长宽分别为 200m 和 50m 的长方形公园周围跑了 6 圈，然后求他在 6 圈中跑了多少距离？

矩形是一个封闭的二维图形，由四个边和四个角组成。矩形对边的长度相等且相互平行。正方形可以被认为是所有边长度相等的矩形的特殊情况。矩形的相邻边相交成直角，即矩形的相邻边所成的角为90°。

矩形的周长

矩形边界所覆盖的总距离称为矩形的周长。矩形的周长是边长的线性度量，用单位、米、厘米、英寸、英尺等表示。矩形的周长是矩形所有四个边的长度之和。

矩形公式的周长

以下公式可用于计算矩形的周长，

Perimeter of a rectangle = 2(l + w) units, 

where ‘l’ is the length and ‘w’ is the width of the rectangle respectively.

问题：一个男孩绕着一个长宽分别为 200 m 和 50 m 的长方形公园跑了六圈。找出他在六轮中跑了多少距离？

解决方案：

这个问题可以通过两种方式解决

方法一：

As the park is rectangular

Therefore,

Perimeter of rectangle = 2 × (Length + Breadth)

Here we are given,

Length of rectangular park = 200 m

Breadth of rectangular park = 50 m

Further,

Perimeter of rectangular park =  2 × (Length + Breadth)

Perimeter of rectangular park = 2 × (200 + 50) = 2 × 250

Perimeter of rectangular park = 500 m

Therefore,

The boys covers a distance of 500 m in a single round of the rectangular park

To find the distance covered by the boy in six rounds of the rectangular park

We will add the perimeter of the rectangular park 6 times as follows;

Distance covered by boy in 6 rounds of the rectangular park = 500 m + 500 m + 500 m + 500 m + 500 m + 500 m

Distance covered by boy in 6 rounds of the rectangular park = 3000 m

Therefore,

The distance covered by the boy of rectangular park in 6 rounds is 3000 m.

方法二：

As the park is rectangular

Therefore,

Perimeter of rectangle =  2 × (Length + Breadth)

Here we are given,

Length of rectangular park = 200 m

Breadth of rectangular park = 50 m

Further,

Perimeter of rectangular park =  2 × (Length + Breadth)

Perimeter of rectangular park = 2 × (200 + 50) = 2 × 250

Perimeter of rectangular park = 500 m

Therefore,

The boys covers a distance of 500 m in a single round of the rectangular park

To find the distance covered by the boy in six rounds of the rectangular park

We will multiply the perimeter of the rectangular park by 6 as follows;

Distance covered by boy in 6 rounds of the rectangular park = 6 × 500 m 

Distance covered by boy in 6 rounds of the rectangular park = 3000 m

Therefore,

The distance covered by the boy of rectangular park in 6 rounds is 3000 m.

示例问题

问题 1：在一个长 150 m、宽 75 m 的长方形体育场内，求一名运动员在 10 圈内跑过的距离？

解决方案：

Here we have to find the distance covered by athlete in 10 laps of a rectangular stadium

We are given that

Length of the stadium = 150 m

Breadth of the stadium = 75 m

To find the distance covered by the athlete in 1 lap we have to calculate the perimeter of the rectangular stadium

Perimeter of rectangular stadium =  2 × (Length + Breadth)

Perimeter of rectangular park = 2 × (150 + 75) = 2 × 225

Perimeter of rectangular park = 450 m

Thus,

Distance covered by athlete in 1 lap is 450

Further 

Distance covered by athlete in 10 lap = 10 × 450

Distance covered by athlete in 10 lap = 4500 m

Hence,

Distance covered by athletes in 10 laps of a rectangular stadium is 4500 m.

问题 2. 计算一个长 75 m、宽 60 m 的矩形学校操场的围栏成本，成本为每米 100 卢比？

解决方案：

Here we have to find the cost of fencing a rectangular school playground

As we know that

Perimeter of rectangle =  2 × (Length + Breadth)

Length of school playground = 75 m

Breadth of school playground = 60 m

Perimeter of school playground = 2 × (75 + 60) = 2 × 130

Perimeter of school playground = 260 m

Further,

Cost of fencing school playground at ₹100 per meter

Cost of fencing school playground = 100 × 260

Cost of fencing school playground = ₹ 26,000

Hence,

Cost of fencing a school playground is ₹ 26,000

问题 3. 如果一个男孩在 5 轮中跑了 3000 m 的矩形公园，如果公园的宽度是 30 m，那么求矩形公园的周长和长度？

解决方案：

Here we have to find the perimeter and breadth of the rectangular park

According to the question

If the boy in 5 rounds covers 3000 m 

Then the distance covered by boy in 1 round = $\frac{3000}{5}$

Then the distance covered by boy in 1 round = 600 m

Then the distance covered by boy in 1 round = Perimeter of the rectangular park

Perimeter of the rectangular park = 600 m

Further,

Perimeter of the rectangular park = 2 × (Length + Breadth)

Breadth = 30 (given)

Perimeter of the rectangular park = 2 × (Length + 30)

$\frac{600 }{2}$ = Length + 30

Length = 300 – 30

Length = 270 m

Therefore,

Perimeter of the rectangular park is 300 m and length of the rectangular park is 270 m

问题 4. 如果一台机器在 10 分钟内完成 1 轮长 600 m 宽 300 m 的矩形场地。如果机器运行 1 小时，那么找到机器在 1 小时内所经过的距离？

解决方案：

Here we have to find the distance covered by the machine of the rectangular field in 1 hour

As per the question

Distance covered by machine in 10 minutes = Perimeter of the rectangular field

Perimeter of the rectangular field = 2 × (Length + Breadth)

Length = 600 m

Breadth = 300 m

Perimeter of the rectangular field = 2 × (600 + 300)

Perimeter of the rectangular field = 2 × 900

Perimeter of the rectangular field = 1800 m

Distance covered by machine in 10 minutes = Perimeter of the rectangular field = 1800 m

1 hour = 60 minutes

Distance covered in 1 minute by the machine = $\frac{1800}{10}$

Distance covered in 1 minute by the machine = 180

Distance covered in 60 minutes by the machine = 60  × 180

Distance covered in 60 minutes by the machine = 10800 m

Therefore,

Distance covered by machine in 1 hour is 10800 m

问题 5. 求一条长 1500 米，宽 400 米的长方形跑道， 6 圈赛车所经过的距离？

解决方案：

Here we have to find the distance covered by racing car in 6 rounds of a rectangular track

We are given that

Length of the track = 1500 m

Breadth of the track = 400 m

To find the distance covered by the racing car in 1 round we have to calculate the perimeter of the rectangular track

Perimeter of rectangular track =  2 × (Length + Breadth)

Perimeter of rectangular track = 2 × (1500 + 400)

Perimeter of rectangular track = 2 × 1900

Perimeter of rectangular park = 3800 m

Thus,

Distance covered by racing car in 1 round is 3800 m

Further

Distance covered by racing car in 6 rounds = 6 × 3800

Distance covered by racing car in 6 rounds = 22800 m

Hence,

Distance covered by racing car in 6 rounds of a rectangular track is 22800 m.