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Verified answer
BD = AC = √(AB² + BC²) = √(320 + 80) = 20 cmAB × BC = BD × AE
8√5 × 4√5 = 20 × AE
AE = 8 cm
DE = FB = BC²/BD = 80/20 = 4
EF = BD - 2 DE = 20 - 8 = 12 cm