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

A line segment of lenght 7.6 cm can be divided in the ratio of 5:8 as follow.
Step 1 Draw line segment AB of 7.6 cm and draw a ray AX making an ancute angle with line

segment AB.
Step 2 Locate 13 (= 5 + 8) points A₁, A₂, A₃, A₄ …… A₁₃, On AX such that A₁A₂ = A₂A₃ and so on.
Step 3 Join BA₁₃.
Step 4 Through the point As, draw a line paraller to BA₁₃ (by making an angle equal to ∠AA₁₃

B) at A₅ intersection AB at point C.
C is the point dividing line segment AB of 7.6 cm in the required ration of 5:8. The lenghts 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 A₅C II A₁₃B. By applying Basic proportionality theorem for
the triangle AA₁₃B, we obtain
AC/CB = AA₅/A₅A₁₃ …(1)
From the figure, it can be observed that AA₅ and A₅A₁₃ contain 5 and 8 equal divisions of line

segments respectively.
AA₅/A₅A₁₃ = 5/8 …(2)
On comparing equations (1) and (2), we obtain AC/CB = 5/8
This justifies the construction.