Question

∆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`.

Answer 1

Construct ∆ABC such that AB = 5.5 cm, BC = 6 cm and CA = 4.5 cm. 
∆ABC and ∆LMN are similar.

Therefore, their corresponding sides are proportional.

∴ `"AB"/"LM" = "BC"/"MN" = "CA"/"NL" = 5/4`

AB = 5.5 cm, BC = 6 cm, CA = 4.5 cm

∴ `5.5/"LM" = 6/"MN" = 4.5/"NL" = 5/4`

∴ `5.5/"LM" = 5/4`

∴ `(5.5 xx 4)/5 = "LM"`

∴ 4.4 = LM

∴ `6/"MN" = 5/4`

∴ `(6 xx 4)/5 = "MN"`

∴ 4.8 = MN

∴ `4.5/"NL" = 5/4`

∴ `(4.5 xx 4)/5 = "NL"`

∴ 3.6 = NL

In ∆ABC, AB = 5.5 cm, BC = 6 cm, CA = 4.5 cm

Now, construct ∆LMN such that LM = 4.4 cm, MN = 4.8 cm and NL = 3.6 cm.