Write True or False and give reasons for your answer.
By geometrical construction,it is possible to divide a line segment in the ratio $2 \sqrt{3} : 2 \sqrt{3}$.
By geometrical construction,it is possible to divide a line segment in the ratio $2 \sqrt{3} : 2 \sqrt{3}$.
(B) False.
The ratio $2 \sqrt{3} : 2 \sqrt{3}$ simplifies to $1 : 1$.
However,the standard geometrical construction method for dividing a line segment in a given ratio $m : n$ requires $m$ and $n$ to be positive integers.
Since $2 \sqrt{3}$ is an irrational number and not a positive integer,it is not possible to divide a line segment in this ratio using the standard ruler and compass construction method.
The ratio $2 \sqrt{3} : 2 \sqrt{3}$ simplifies to $1 : 1$.
However,the standard geometrical construction method for dividing a line segment in a given ratio $m : n$ requires $m$ and $n$ to be positive integers.
Since $2 \sqrt{3}$ is an irrational number and not a positive integer,it is not possible to divide a line segment in this ratio using the standard ruler and compass construction method.
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