D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 3 cm, BD = 5 cm, BC = 12.8 cm and DE|| BC. Then

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D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 3 cm, BD = 5 cm, BC = 12.8 cm and DE|| BC. Then length of DE is

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Adalynn 4 weeks 2021-08-14T02:59:57+00:00 1 Answer 0 views 0

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    2021-08-14T03:01:42+00:00

    Given :

    A ∆ABC in which DE // BC. AD = 2cm, BD = 3 cm and BC = 7.5 cm.

    To find :

    The length of DE

    _______________________________________

    Since, DE is parallel to BC

    → angle ADE = angle ABC (corresponding angles)

    → angle AED = angle ACB (corresponding angles)

    Hence, by AA criterion of similarity,

    ∆ADE ~ ∆ABC

    ratio of corresponding sides of similar triangles are equal.

    AD/AB = DE/BC

    AB = AD + DB

    AB = 2 + 3 = 5 cm

    So,

    2/5 = DE/7.5

    DE = 2/5 × 7.5

    DE = 2 × 1.5

    DE = 3 cm.

    Hence, the length of side DE is 3 cm.

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