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 B_{1} , B_{2} , B_{3}, B_{4}, and B_{5} at equal distance is marked on BX.

Step 4. B_{3} is joined with C to form B_{3} C as 3 point is smaller. B_{5} C_{1} is drawn parallel to B_{3} C as 5 point is greater.

Step 5:C_{1}A_{1}is drawn parallel to CA.

Thus, A_{1}BC_{1} is the required triangle.

**Justification:**

Since the scale factor is ,

We need to prove,

By construction,

… (1)

Also, A_{1}C_{1} is parallel to AC.

So, this will make same angle with BC.

∴ ∠A_{1}C_{1}B = ∠ACB …. (2)

Now,

In ΔA_{1}BC_{1} and ΔABC

∠ B = ∠ B (common)

∠A_{1}C_{1}B = ∠ACB (from 2)

ΔA_{1}BC_{1}∼ ΔABC

Since corresponding sides of similar triangles are in same ratio.

From (1)

Hence construction is justified.

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