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

Steps of Construction :
(i)     Draw AB = 5.6 cm
(ii)    At a draw an acute ∠BAX below base AB.

(iii)    On AX make 5 + 8 i.e. 13 equal parts and mark them as A₁, A₂, A₃, A₄,... A₁₃

(iv)    Join B to A₁₃. From A₅ draw A₅C || A₁₃B. C is the required point of division and AC : CB = 5 : 8.

On measuring, we get
AC = 3.1 cm,
CB = 4.5 cm
Justification :

[Using basic proportionally theorem]

Therefore,    

This shows that C divides AB in the ratio 5 : 8.