Question

Is it possible to divide a line segment in the ratio 2√5:3 by geometrical construction? Give reasons.​

Answer 1

Answer:

a line segment can be divide in the ratio $2\sqrt{5 }:3$

Step-by-step explanation:

given ratio  2$\sqrt{5}$ : 3

finding out if it is possible to divide a line segment in to the given ratio  

Line segment :

  a straight line with two end points is know as line segment

  in a line segment the length of the line is not changeable so it can be divided into "n" time ( it is possible when n need to be a is a positive number)

  the given ratio  = $2\sqrt{5} : 3$  

      $\sqrt{ 5}$  is will be in between  $\sqrt{ 4}$  and $\sqrt{ 9}$

                      ⇒   $\sqrt{4 } <\sqrt{5} < \sqrt{9}$                        

                         2 < $\sqrt{ 5}$ < 3             [initially $\sqrt{5}$ =2.236079  so we will take

     ∴     $2\sqrt{5} : 3$ = 2(2.2) : 3                               up to 2 decimals  $\sqrt{5} =2.2$

                      ⇒    4.4:3                    

  by using 4.4 : 3  we can divide a line segment

    so we can divide a line segment in the ratio $2\sqrt{ 5} :3$