A line segment is divided into four equal parts forming an arithmetic progression . The sum of the lengths of 3rd and 4th parts is three times the sum of the length of first two parts. If the length of 4th part is 14 cm . Find the total length of the line segment.
Answers
Answer:
Step-by-step explanation:
Total length of the line segment is 32 cm
Solution:
A line segment is divided into four equal parts forming an arithmetic progression
Let the four parts be:
a , a + d , a + 2d , a + 3d
The sum of the lengths of 3rd and 4th parts is three times the sum of the length of first two parts
a + d + a + 2d = 2(a + a + d)
2a + 3d = 4a + 2d
d = 2a
The length of 4th part is 14 cm
Therefore,
a + 3d = 14
Substitute d = 2a
a + 3(2a) = 14
a + 6a = 14
7a = 14
a = 2
Thus,
d = 2a
d = 2(2)
d = 4
Find the total length of the line segment
Total length = a + a + d + a + 2d + a + 3d
Total length = 4a + 6d
Total length = 4(2) + 6(4)
Total length = 8 + 24
Total length = 32
Thus total length of the line segment is 32 cm
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A line segment is divided into four parts forming an Arithmetic progression.
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