Given some line segment , whose length you do not know, construct such that the length of is twice that of .

Question

KnowledgeBoat · Accepted Answer

Steps: 1. Draw a line segment AB of any length. 2. Draw any line l and mark a point P on it. 3. Place the pointer end of the compass at the point A and open the compass till the pencil end exactly coincides with the point B. This opening of the compass gives the length of the segment AB. 4. Without changing the opening of the compass, place the pointer end at the point P and draw an arc to cut the line l at the point R. So, PR = AB. 5. Again, without changing the opening of the compass, place the pointer end at the point R and draw another arc to cut the line l at the point Q. So, RQ = AB. Thus, PQ = PR + RQ = AB + AB = 2 × AB. Hence, PQ is the required line segment whose length is twice that of AB.

Mathematics

Given some line segment $\overline{AB}$ , whose length you do not know, construct $\overline{PQ}$ such that the length of $\overline{PQ}$ is twice that of $\overline{AB}$ .

Constructions

Answer

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Mathematics

Given some line segment AB‾\overline{AB}AB, whose length you do not know, construct PQ‾\overline{PQ}PQ​ such that the length of PQ‾\overline{PQ}PQ​ is twice that of AB‾\overline{AB}AB.