Question

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

Answer 1

$\huge{\pink{\green {\sf\boxed{ANSWER = 32}}}}$

$\huge{\pink {\sf\boxed{Step\: by\: step\: explanation}}}$

Fourth part: 14

Third part: 14 - 4 = 10

Second part: 10 - 4 = 6

First part: 6 - 4 = 2

14 + 10 = 24 [6 + 2 = 8 ]

8 * 3 = 24

24 + 8 = $\small {\pink{\green {\sf\boxed{34}}}}$

Answer 2

Solution :

Let the four pats of the line segment be

a-3d,a-d,a+d,a+3d

according to the question

(a+d+a+3d) = 3(a-3d+a-d)

2a+4d= 3(2a-4d)

2(a+2d) = 6(a-2d)

a+2d=3a-6d

2d+6d=3a-a

2a = 8d

a = 4d

a+3d = 14

4d+3d = 14

7d = 14

d = 2

a = 4d

a = 4×2

a = 8

length of the line segment

a-3d+a-d+a+d+a+3d

= 4a

= 4×8

= 32 cm

Hence , length of the line segment is 32 cm

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