Let us draw the mean proportional of the following line segment and let us measure the values of the mean proportionals in each case with help of a scale:

12cm., 3cm.

Construction steps:

1. Draw a line segment AX with length greater than (12 + 3 = 15 cm).

2. From A, mark a point B on AX such that AB = 12 cm and from B mark a point C such that BC = 3 cm

3. Draw the perpendicular bisector of AC, such that it cuts AC at O.

4. Taking OA = OC as radius and O as center draw a semicircle.

5. Draw BD ⊥ AC such that, point D lies on the semicircle and

Here, BD is the mean proportional of AB and BC, and By construction AB = 12 cm and BC = 3 cm.

With the help of scale, we measure BD = 6 cm [Appx]