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

Step 1: Draw line segment AB = 7.6 cm

Step 2: Draw a ray AC making an acute angle with line segment AB .

Step 3: Along AC, divide (5+8) 13 equals points

A₁,A₂,A₃,……………….,A₁₃ on AX such that

AA₁=AA₂=A₂A₃ and so on .

Step 4: Join BA₁₃

Step 5: Through the point A₅, draw a line parallel to BA₁₃ (by making an angle equal to ∠AA₁₃B) at A₅ intersecting AB at point D.

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

The lengths of AD and DB 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 A₅D∥A₁₃B. By applying Basic proportionality theorem for

From the figure, it can be observed that AA₅ and A₅A₁₃ contain 5 and 8 equal divisions of line segments respectively.

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

This justifies the construction.