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Answer :
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