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# 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