draw a line segment of lenght 7.6 cm and divide it in the ratio 5:8 measure the two parts. and give justification also

A line segment of length 7.6 cm can be divided in the ratio of 5:8 as follows.**Step 1** Draw line segment AB of 7.6 cm and draw a ray AX making an acute angle with line segment AB.**Step 2** Locate 13 (= 5 + 8) points, A_{1}, A_{2}, A_{3}, A_{4 }…….. A_{13}, on AX such that AA_{1} = A_{1}A_{2 }= A_{2}A_{3} and so on.**Step 3** Join BA_{13}.**Step 4 **Through the point A_{5}, draw a line parallel to BA_{13} (by making an angle equal to ∠AA_{13}B) at A_{5} intersecting AB at point C.

C is the point dividing line segment AB of 7.6 cm in the required ratio of 5:8.

The lengths of AC and CB can be measured. It comes out to 2.9 cm and 4.7 cm respectively.**Justification**

The construction can be justified by proving that

By construction, we have A_{5}C || A_{13}B. By applying Basic proportionality theorem for the triangle AA_{13}B, we obtain

… (1)

From the figure, it can be observed that AA_{5} and A_{5}A_{13} contain 5 and 8 equal divisions of line segments respectively.

… (2)

On comparing equations (1) and (2), we obtain

This justifies the construction.