Steps of Construction:
1. Draw a line segment AB of length 7. 6cm.
2. Draw a ray AZ making an acute angle with the line AB.
3. As we have to divide the line in the ratio of 5:8. So we will make 5+8 = 13 points along AX.
4. Along AX we mark 13 arcs taking A as starting point for the first, A1 as starting point for second and so on till A13.
5. Join the A13B.
6. With the help of these arcs, this line can be divided into 13 equal points.
7. In our case of 5:8, we join the 5th point i. e. A5 with the line AB such that the line A5P is parallel to line A13B.
8. P is the required point, the point that divides the line in a ratio of 5:8.
Length of AP = 2. 9cm (approximately )
Length of PB = 4. 7cm (approximately )
AP+PB = 2. 9+4. 7 = 7. 6 = AB.
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