in triangle ABC DE is parallel to Bc if AD is equal to 4 Db= 6 and EC= 12 then the value of AE=​

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in triangle ABC DE is parallel to Bc if AD is equal to 4 Db= 6 and EC= 12 then the value of AE=​

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Aaliyah 3 weeks 2021-11-03T20:26:46+00:00 1 Answer 0 views 0

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    2021-11-03T20:27:59+00:00

    Step-by-step explanation:

    ANSWER

    REF.Image.

    In △ADE and △ABC

    ∠A=∠A [common]

    Since DE∥BC, DB and EC will

    act as traversals

    ∴∠ADE=∠ABC  

    and ∠AED=∠ACB [corresponding angles]

    So, by similarity of triangles : △ADE∼△ABC[By AAA citiesion]

    ∴ABAD=ACAE(x+2)+(3x+16)x+2=x+(3x+5)x

    (4x+18)(x+2)=(4x+5)x⇒(x+2)(4x+5)=x(4x+18)

    ⇒4×2+5x+8x+10=4×2+18x⇒5x=10⇒x=2

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