Answer :

Step 1. At first drawn a base line BC of length 5.5 cm with the help of scale.



Step 2. Taking B as center draw an arc of radius 5 cm with the help of compass. Similarly taking C as center draw a arc of radius 6.5 cm with the help of compass.


Join AB and AC thus completing the triangle ABC.



Step 3. A ray BX is drawn making an acute angle with BC opposite to vertex A. Five points B1 , B2 , B3, B4, and B5 at equal distance is marked on BX.



Step 4. B3 is joined with C to form B3 C as 3 point is smaller. B5 C1 is drawn parallel to B3 C as 5 point is greater.



Step 5:C1A1is drawn parallel to CA.



Thus, A1BC1 is the required triangle.


Justification:


Since the scale factor is ,


We need to prove,



By construction,


… (1)


Also, A1C1 is parallel to AC.


So, this will make same angle with BC.


A1C1B = ACB …. (2)


Now,


In ΔA1BC1 and ΔABC


B = B (common)


A1C1B = ACB (from 2)


ΔA1BC1 ΔABC


Since corresponding sides of similar triangles are in same ratio.



From (1)



Hence construction is justified.

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