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

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