Question

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 $\overline{AB}$.

Answer 1

Construct the required line segment based on given information :

Follow the given steps to construct $\overline{PQ}$:

1. Consider line segment $\overline{AB}$ as

2. Take a compass, put the pointer side on $A$ and the pencil side on $B$ , and measure the length of $\overline{AB}$.

3.Draw any line $l$ and mark a point $P$ anywhere on the line

4. Place the compass pointer on $P$ and draw an arc $X$ measuring the length of $\overline{AB}$ on the line $l$.

5.Again draw an arc $Q$ from $X$ of same length.

Hence, the length of $\overline{PQ}$ is twice of $\overline{AB}$.