If efgh is the inscribed rectangle of rectangle ABCD, and EF: FG = 3:1, AB: BC = 2:1, then ah: AE=______ ．

Let ah = a, AE = B, ∵ - CFG = - DGH = - ahe = - Feb, ∵ hae = - FCG = 90 °, AE = CG, ≌ - ahe ≌ - CFG (AAS); from the equality of triangles, ∵ CGF ≌ BFE, ∵ ebfc = effg = fbgc = 3, namely EB = 3A, BF = 3b, ∵ AB: BC = 2:1, ≌ 3A + B3b + a = 2, namely a = 5b, ah

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