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