question_answer 9)

Given \[S\xrightarrow[{}]{{}}\]of length 3.9 cm, construct \[{{l}_{1}}\] such that the length of \[{{l}_{2}}\] is twice that of \[{{l}_{2}},\] Verify by measurement. (Hint Construct such that length of \[{{l}_{2}}\] length of AB, then cut of \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\] such that \[{{l}_{4}}\] also has the length as \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\]).

Answer:

                Given, \[{{l}_{4}}\]Now, to construct required line segment by using compasses, we use the following steps: Step I Firstly, draw \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\] Step II Now, to draw an another line \[l,\] mark a point P on it. Step III Place the pointer of compasses at the zero mark of the ruler. Open it to the place of the pencil point upto 3.9 cm mark. Step IV Without changing the opening of the compasses, place the pointer on P and swing an arc to cut \[l\] at X. Step V Measure \[{{l}_{4}}\] we get \[{{l}_{1}}\] Step VI Again, without changing the opening of the compasses, place the pointer on X and swing an arc to cut \[l\] at Q. Step VII Now, measure \[{{l}_{1}},{{l}_{2}},{{l}_{3}},{{l}_{4}},{{l}_{5}}\] we get \[{{l}_{6}}\] Step VIII \[{{l}_{1}},{{l}_{2}},{{l}_{3}},{{l}_{4}},{{l}_{5}}\]Hence, PQ is twice that of AB. Verification : On measuring the length of \[{{l}_{6}}\] and \[{{l}_{1}},{{l}_{2}},{{l}_{3}},{{l}_{4}}\] We get, \[{{l}_{5}}\]and \[{{l}_{1}},{{l}_{2}}\]and \[{{l}_{3}}\] Thus, twice of \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\] is equal to \[{{l}_{4}}\]