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Mathematics

D and E are points on the sides AB and AC respectively of ΔABC. In which of the following cases DE ∥ BC?

  1. AD = 3 cm, BD = 8 cm, AC = 8 cm, AE = 3 cm

  2. AD = 5 cm, BD = 6 cm, AE = 6 cm, CE = 5 cm

  3. AB = 18 cm, AD = 8 cm, AE = 12 cm, EC = 15 cm

  4. none of these

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Answer

On a map drawn to a scale of 1 : 25000, a triangular plot LMN of land has the following measurements : Similarity of Triangles, RSA Mathematics Solutions ICSE Class 10.

Checking option 3,

Given,

In ΔABC, DE is parallel to BC if and only if it divides the sides AB and AC in the same ratio

From figure,

DB = AB - AD = 18 - 8 = 10 cm

ADDB=810=45\dfrac{AD}{DB} = \dfrac{8}{10} = \dfrac{4}{5}

AEEC=1215=45\dfrac{AE}{EC} = \dfrac{12}{15} = \dfrac{4}{5}

∴ADDB=AEEC\therefore \dfrac{AD}{DB} = \dfrac{AE}{EC}

AB = 18 cm, AD = 8 cm, AE = 12 cm, EC = 15 cm DE is parallel to BC holds true.

Hence, option 3 is the correct option.

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