Question

Divide a line-segment into three parts in the ratio 2:3:4 in the same order.

Answer 1

Let the segment length is unity.

hence as shown in attachment

lenght of AP = 2x ,PQ = 3x,QB = 4x.

hence, 2x+3x+4x = 1

so, x = $\frac{1}{9}$

Finally, AP = $\frac{2}{9}$

PQ = $\frac{1}{3}$

QB = $\frac{4}{9}$

Answer 2

Steps of Construction:
1. Draw a line AB of any length.
2.Draw a ray AX making an acute angle with AB.
3. We have to divide line in ratio of 2:3:4. So we make 2+3+4 =9 equal arcs on ray AX.
4. Taking A as center, cut an arc on ray AX. Mark the point as A1.
5. Now, with the same radius cut an arc on AX with A1 as center.
6. Mark till A9.
7. Join A9 with B.
8. As we have to divide in 2:3:4, we draw a line from A2 and A5 parallel to A9B.
9. The point where it cuts AB is P and Q
Here, AP : PQ : QB = 2 : 3 : 4