Question

Draw a line, 6 centimetres long and divide it in the ratio 2 : 3 : 4.

Answer 1

The steps of construction to divide a line segment of length 6 cm in the ratio 2:3:4 are as follows:

1) Draw a line segment AB of length 6 cm.

2) At B, draw BY perpendicular to AB.

3) Taking A as the centre and 9 cm (sum of ratios) as the radius, draw an arc on BY. The point where the arc cuts BY is named as R. Join AR.

4) Taking A as the centre and 2 cm as the radius, draw an arc on AR and name it as P.

5) Taking P as the centre and 3 cm as the radius, draw an arc on AR and name it as Q. The remaining length QR = 9 cm − 2 cm − 3 cm = 4 cm.

6) Draw PC and QD parallel to RB.

We have obtained that AC:CD:DB = 2:3:4.

Thus, points C and D divide line segment AB of length 6 cm in the ratio 2:3:4.