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

Construction according to the required data is done as follows:
Step1: Draw a line segment AB=7.6 cm and at point A draw a ray AC making acute angle with AB.

Step 2: As shown in figure, start locating 13 marks (5+8) as \(A_1,A_2,A_3,.....A_{13} \), such that \(AA_1=AA_2=AA_3 \)..and so on.

Step 3: Now join the points \(A_{13} \) and B.

Step 4: From point \(A_5 \), draw a line parallel to \(A_{13}B\) and mark the intersection point as P.
Step 5: Measure AP and PB. we will find AP= 2.9cm and PB =4.7cm(approx) which are in approx ration of 5:8.



Justification:

In \(ΔAA_5P and △AA_13B \) we have,

\(A_5P ∥ A_{13}B\)

\(\frac{AP}{BP}=\frac{AA_5}{A_5A_{13}} \)
(By the Basic proportionality theorem)

\(\frac{AP}{BP}=\frac{5}8 \) {∵ \(\frac{AA_5}{A_5A_{13}}=\frac{5}8 \)}

\(\therefore \) , AP:BP=5:8