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5 March, 19:04

Given: △ABC, D∈ AB, E∈BC, F∈AC, DE∥AC, AD∥FE, AD=6, DE=5, AB=17. Find: AC

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  1. 5 March, 19:17
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    AC = 7.73

    Step-by-step explanation:

    ∵ DE / / AC

    ∴ m∠BDE = m∠BAC ⇒ corresponding angles

    ∴ m∠BED = m∠BCA ⇒ corresponding angles

    ∵ ∠B is common angle

    ∴ Δ BDE is similar to Δ BAC

    ∴ BD/BA = DE/AC = BE/EC

    ∵ AD = 6 and AB = 17

    ∴BD = 17 - 6 = 11

    ∵ DE = 5

    ∴ 11/17 = 5/AC

    ∴ AC = (5 * 17) : 11 = 7.7272 ≅ 7.73
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