Question

the line segment is divided into four parts forming an AP . The sum of the lengths of 3rd and 4th parts is three times the sum of the lengths of first two parts. If the length of fourth parts is 14cm, find the total length of the line segment​

Answer 1

Step-by-step explanation:

Let the line is divided into four parts a

1

,a

2

,a

3

,a

4

a

3

+a

4

=3(a

1

+a

2

)

a

4

=14

(a+2d)+14=3(a+a+d)

a+2d+14=6a+3d

14=5a+d………………….(1)

a

4

=14

a+3d=14………………….(2)

From (1) and ( 2 ) a+3d=5a+d

2d=4a

d=2a

From (2)

a+3d=14

a+3(2a)=14

a+6a=14

7a=14

a=2

d=4

a

1

=2

a

2

=6

a

3

=10

a

4

=14

Therefore, length of the line segment is 2+6+10+14=32cm