#### Question

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

#### Solution

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

`(AC)/(CB) = 5/8`

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

`(AC)/(CB) =(`

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

`:. (`

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

`(AC)/(CB) = 5/8`

This justifies the construction