Answer :

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 A_{13}.

5. Join the A_{13}B.

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 5^{th} point i. e. A5 with the line AB such that the line A_{5}P is parallel to line A_{13}B.

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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