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## Number of Trees Planted Along a Road

Number of trees that can be planted along a road or around a field .

Number of poles/ lampposts along a road or around a field .

Number of coaches or gangway connections (links) in a train.

**The fact that in all the above arrangements each object is put at a regular distance can help****us find –****✓ Number of trees , poles , lampposts.****✓ Length of road , side of field, perimeter, or area of a field.****✓ Distance between two objects**

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**Case 1**

When trees/pillars are arranged in a straight line

Let us consider a situation where gap between two objects is 1 m

Two poles / trees / lampposts arranged in a row.

Distance = 1m , number of poles/trees n = 2

Three poles / trees / lampposts arranged in a row.

Distance = 2m , number of poles/trees n = 3

6 poles / trees / lampposts arranged in a row.

Distance = 5m , number of poles/trees n = 6

This can be generalised as

1) Number of trees , poles , lamp posts along a road or along a straight line

N = number of intervals + 1

2) Number of Intervals/gaps/ links between trees(poles or any other object ) =Total distance ÷ length of each interval(gap)

3) Total distance /Length of the road/ length of wire or rope required to surround a

field.

D = total number of Intervals or gaps x length of each gap

**Case 2**

Number of trees/poles that can be planted/erected around a circular path or around a field .

In the above figure number of trees = 6

Number of Intervals = 6

In a closed arrangement number of intervals = number of trees/poles/lampposts

**Example 1:**

How many trees can be planted along a 200m long road if the distance between each tree

should be kept.

a ) 1 metre

b ) 5 metre

**Solution:**

a) Regular distance between trees = 1 m

Total distance = 200 m

Number of intervals = 200/1= 200

Number of trees arranged in a line n = number of intervals +1=200+1=201

b) Regular distance between trees = 5 m

Total distance = 200 m

Number of intervals (distance) = 200/5= 40

Number of trees arranged along the road n = number of intervals +1=40+1=41

**Example 2:**

A company gets a contract for installing lampposts along a road. Distance between two

continuous lampposts should be kept 2.5 metres .What is the total number of lampposts

that should be ordered to the supplier if the length of the road is 400m?

**Solution:**

Regular distance between lampposts = 2.5 m

Total distance = 400 m

Number of intervals = 400m ÷ 2.5m= 160 intervals (gap)

Number of lamp posts arranged along the road n = number of intervals +1=160+1=161

Example 3:

Certain number of lampposts are to be installed around a circular park with diameter= 14m.

What is the number of lampposts required if a regular gap of 4m must be maintained between

two lampposts?

Solution:

Radius of the circular path = r = d / 2 = 14 / 2 = 7 m

Circumference of the path = 2∏r = 2 x 22/7 x 7 = 44 m

Here total length of path = circumference of the circular path=44

Total number of intervals = Total length of path / Length of each interval = 44m / 4m = 11

Number of trees = Number of intervals= 11