Lets understand the construction steps by doing a construction for a sample problem

Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.

**Solution:** Draw a line segment AB = 7.6 cm.

Draw a ray AX which makes an acute angle with AB.

Locate 13 points (5 + 8) A_{1}, A_{2}, A_{3}, …….A_{13} on AX so that;

AA_{1} = A_{1}A_{2} = A_{2}A_{3} = A_{3}A_{4} = A_{4}A_{5} = A_{5}A_{6} = A_{6}A_{7} = A_{7}A_{8} = A_{8}A_{9} = A_{9}A_{10} = A_{10}A_{11} = A_{11}A_{12} = A_{12}A_{13}

Join A_{13} to B.

Through the point A_{5}, draw a line A_{5}C || A_{13}B; which intersects AB at point C.

We get; AC : CB = 5 : 8

AC = 2.92 cm and CB = 4.68 cm