Answer:
Given, \[{{l}_{4}}\] and \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\] Now, to construct required line segment \[{{l}_{4}}\] we use the following steps: Step I Firstly, draw \[{{l}_{1}}\]and \[{{l}_{1}},{{l}_{2}},{{l}_{3}},{{l}_{4}},{{l}_{5}}\] 
Step II Now, place the pointer of compasses on C of pencil on D. The opening of the instrument gives the length of \[{{l}_{6}}\] i.e. 3.4 cm. Step III Without changing the opening of the compasses place the pointer on A and swing an arc to cut \[{{l}_{2}}\] at R. 
Step IV Thus, \[{{l}_{1}},{{l}_{2}},{{l}_{3}},{{l}_{4}},{{l}_{5}}\] and \[{{l}_{6}}\]is the difference between the length of \[{{l}_{1}},{{l}_{2}},{{l}_{3}},{{l}_{4}}\] and\[{{l}_{5}}\] Step V Now, draw a line \[l\] and mark a point X on it. Step VI Place the pointer of compasses on R and of pencil on B. The opening of the compasses gives the length of \[{{l}_{6}}\]. Step VII Without changing the opening of the compasses, place the pointer on X and swing an arc to cut \[l\] at Y. Thus, \[{{l}_{1}},{{l}_{2}}\] is a line segment whose length is equal to the difference between the lengths of \[{{l}_{3}}\] and \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\] 
Verification By actual measurement, we have \[{{l}_{4}}\] Now, \[{{l}_{1}}\] \[{{l}_{2}}\]\[{{l}_{1}}\] i.e. length of \[{{l}_{1}}\] The difference of lengths \[{{l}_{2}}\] and \[S\xrightarrow[{}]{{}}\] Hence, verified.
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