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प्रश्न
∆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`.
उत्तर
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.
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