ABC ~ LMN. In ABC, AB = 5.5 cm, BC = 6 cm, CA = 4.5 cm. Construct ABC and LMN such that BC /MN = 5/ 4 .

Rough figure is shown below.

Given ABC and LMN are similar.
their corresponding sides are proportional.
AB/LM = BC/MN = AC/LN
Given BC/MN = 5/4
AB/LM = BC/MN = AC/LN = 5/4
As the sides AB, BC and AC are known we can find lengths of sides LM,MN and LN.
Given AB = 5.5 , BC = 6 , CA = 4.5
Substitute values of AB, BC and CA
5.5/LM = 6/MN = 4.5/LN = 5/4
5.5/LM = 5/4
LM = 5.5×4/5 = 4.4 cm
6/MN = 5/4
MN = 6×4/5 = 4.8 cm
4.5/LN = 5/4
LN = 4.5×4/5 = 3.6 cm
Now construct LNM such that LM = 4.4 cm, MN = 4.8 cm and LN = 3.6cm.