Question

A line was measured by a 20 m chain which was accurate before starting the day's work, Allier chaining 900 m,
the chain was found to be 6 cm too long. After chaining a total distance of 1,575 m, the chain was found to be 14
cm too long. Find the true distance of the line.
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Answer 1

Answer:

TRUE DISTANCE = 1,579.725 m

Answer 2

Answer:

True distance of line is 1579.725m

Explanation:

Given,

Length of Chain(L)=20m

We solve this problem in two parts

(i)First Part

Given that, after chaining a distance of 900m,It was found that chain is 6cm too long

Therefore,mean elongation is given by

$e_{1} = 20 + \frac{0 + 0.06}{2} = 20 + 0.03 = 20.03m$

Now true length of line is given by,

$L _{1} = \frac{20.03}{20} \times 900 = 901.35m$

(ii)Second Part

Given that,after chaining a total distance of 1575m,the chain was found to be 14cm too long

Therefore,mean elongation is given by

$e_{2} = 20 + \frac{0.06 + 0.14}{2} = 20 + 0.1 = 20.1m$

Now true length of line is given by

$L _{2} = \frac{1575 - 900}{20} \times 20.1 = 678.375m$

Therefore total true length is given by Sum of lengths of first and second parts

Therefore,

TL=901.35m+678.375m=1579.725m

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