question_answer 1)

Given, some line segment \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\] whose length you do not know, construct \[{{l}_{4}}\] such that the length of \[{{l}_{1}}\] is twice that of \[{{l}_{1}},{{l}_{2}},{{l}_{3}},{{l}_{4}},{{l}_{5}}\]

Answer:

                To make \[{{l}_{6}}\] we use the following steps: Step I First of all, draw a line segment AB, whose length is not known. Step II Fix the pointer of compasses on A and the pencils end on B. The opening of the instrument now gives the length of \[{{l}_{1}},{{l}_{2}},{{l}_{3}},{{l}_{4}},{{l}_{5}}\] Step III Draw any line \[l\]. Choose a point P on \[l,\] without changing the compasses setting, place the pointer on P, swing an arc that cuts \[l\] at point R. Step IV Now, place the pointer on R and without changing the compasses setting, swing another are that cuts \[l\] at a point Q. Step V Thus, \[{{l}_{6}}\] is the required line segment whose length is twice that of \[{{l}_{1}},{{l}_{2}},{{l}_{3}},{{l}_{4}}\] Hence, \[{{l}_{5}}\]