Chapter 10.2, Problem 10CE

To determine

To describe: the construction of the following triangle whose sides are in the ratio $1:2:\sqrt{5}$ .

Explanation of Solution

Given Information:

Given figure,

  

Calculation:

Procedure:

1. Draw a line segment $\overline{AB}$ of any length.
2. Draw a line $l$ .
3. Let $P$ be a point on the line.
4. Measure the length of $AB$ .
5. Use this measure as radius and $P$ as center draw two arcs intersecting the line $l$ . Let this points be $Q$ and $S$ .
6. Use a suitable radius and $Q$ as center, draw an arc.
7. With same radius and $S$ as center, draw an arc intersecting the arc drawn using $Q$ as center. Label the point of intersection as $X$ .
8. Draw $\overline{PX}$ .
9. Use the length of $AB$ as radius and $P$ as center draw an arc on $\overline{PX}$ . Label the point of intersection as $Y$ .
10. Use the length of $AB$ as radius and $Y$ as center, draw an arc on $\overline{PX}$ . Label the point of intersection as $R$ . Thus, length of $\overline{PR}=2AB$ .
11. Draw $\overline{QR}$ .

Thus, triangle $PQR$ is obtained whose sides are in the ratio $1:2:\sqrt{5}$ .

The figure drawn is shown below.