Question

Draw a line segment of \[6cm\] and divide it in the ratio $3:2$.

Answer 1

Hint: Whenever we have this type of problem, first draw a line of given length then locate a point in the same plane which makes an angle of less than $90$ degrees with respect to the line segment. Then make $5$ equal parts so that the sum of those should be equal to the given length of the line. And now divide as per the requirement using parts of the length.

Complete step by step answer:
In this type of question first draw a line segment be $AB$ of given length \[6cm\] , as shown in the below diagram.

Now, we need to divide the line segment in the ratio $3:2$ . In order to do this we need to follow some steps or procedures.
First, locate a point say $X$ at any point such that the angle of $BAX$ should be less than the $90$ degrees that is which makes an acute angle, and join the points $AX$ . As shown in the below figure.

In order to divide the line segment in the ratio $3:2$, we need to make the line segment $AX$ $5$ equal parts (because $3 + 2 = 5$) in such a way that on adding all the $5$ parts we should get the length equal to the line segment $AB$ that is \[6cm\]. Which is shown as in the below figure.

As shown in the above diagram the $5$ equal parts are equal to each other. Sum of the these are equal to the length of the line segment $AB$ , that is $A{x_1} + {x_1}{x_2} + {x_2}{x_3} + {x_3}{x_4} + {x_4}{x_5} = 6cm$.
Now join the points $B$ and ${x_5}$ , then draw a line which is parallel to $B{x_5}$ from the point ${x_3}$ which intersect the line segment $AB$ at a point $C$, as shown below.

Therefore, the line segment $AB$ is divided in the ratio $3:2$ at point $C$. Hence $AC:CB = 3:2$.

Note:
The given question can be solved in another way also, that is as follows:
To divide the line segment in the ratio $3:2$we have
$6 \times \dfrac{3}{5} = \dfrac{{6 \times 3}}{5} = 3.6$ and $6 \times \dfrac{2}{5} = \dfrac{{6 \times 2}}{5} = 2.4$.
Now, we will be having a point $C$ where $3.6cm$ from left and $2.4cm$ from right side which divides the line segment $AB$ in the ratio $3:2$.