# A boy runs six rounds around a rectangular park whose length and breadth are 200 m and 50m, then find how much distance did he run in six rounds?

Rectangle is a closed two-dimensional figure that comprises of four sides and four corners. The length of the opposite sides of the rectangle is equal and parallel to each other. A square can be considered as a special case of a rectangle where all the sides are equal in length. The adjacent sides of a rectangle intersect at the right angle that is, the angle formed by the adjoining edges of a rectangle is 90°.

**Perimeter of Rectangle**

The total distance covered by the boundaries of the rectangle is known as the perimeter of the rectangle. The perimeter of a rectangle is a linear measure in terms of sides, denoted by the units, meters, centimeters, inches, feet, etc. The perimeter of the rectangle is obtained by the summation of the length of all four sides of the rectangle.

**Perimeter of Rectangle formula**

The following formula can be used to compute the perimeter of the rectangle,

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

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

**Problem: A boy runs six rounds around a rectangular park whose length and breadth are 200 m and 50 m. Find how much distance did he run in six rounds?**

**Solution:**

This problem can be solved by two approaches

**Approach 1:**

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.

**Approach 2: **

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.

### Sample Problems

**Problem 1: Find the distance covered by an athlete in 10 laps of a rectangular stadium of length 150 m and breadth is 75 m?**

**Solution:**

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.

**Problem 2. Calculate the cost of fencing a rectangular school playground of length 75 m and breadth 60 m at the cost of **₹**100 per meter?**

**Solution:**

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

**Problem 3. If a boy runs 3000 m of a rectangular park in 5 rounds and if the Breadth of the park is 30 m then find the perimeter and length of the rectangular park?**

**Solution:**

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 =

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)

= 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

**Problem 4. If a machine completes 1 round of the rectangular field of length 600 m and breadth 300 m in 10 minutes. If the machine is operated for 1 hour then find the distance covered by the machine of the field in 1 hour?**

**Solution:**

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 =

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

**Problem 5. Find the distance covered by racing car in 6 rounds of a rectangular track of length 1500 m and breadth is 400 m?**

**Solution:**

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.