Q10. - Geometry

Question

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

Step-by-Step Solution

Answer

The construction for the required figure is mentioned in the below steps.

Step 1. Given information.

Given figure      

Step 2. Concept Used.

Calculation.

 Procedure: 

1. Draw a line segment $\overrightarrow{AB}$ 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 point 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 $\overrightarrow{PX}$.
9.  Use the length of $AB$ as radius and $P$ as center draw an arc on $\overrightarrow{PX}$.  Label the point of intersection as $Y$.
10.  Use the length of AB as radius and X as center, draw an arc on $\overrightarrow{PX}$. Label the point of intersection as $R$. Thus, length of $\overrightarrow{PR}=2AB.$  
11. Draw  $\overrightarrow{QR}$.

 

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

The figure drawn is shown below-