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It is known that: as shown in the figure, in RT △ ABC, ∠ C = 90 °, BC = 4, AC = 8, the point D is on the hypotenuse AB, make de ⊥ AC, DF ⊥ BC respectively, the perpendicular feet are e, f respectively, and get the quadrilateral decf, let de = x, DF = y. (1) use the algebraic formula containing y to express AE, and get AE=______ (2) find out the function relation between Y and X, and find out the value range of X; (3) let the area of quadrilateral decf be s, find out the maximum value of S
(1) It is known that decf is rectangular, so EC = DF = y, AE = 8-ec = 8-y; (2) ∵ de ∥ BC, ∥ ade ∥ ABC, ∥ DEBC = aeac, that is, X4 = 8 − Y8, ∥ y = 8-2x (0 ＜ x ＜ 4); (3) s = xy = x (8-2x) = - 2 (X-2) 2 + 8, ∥ when x = 2, s = - 2 (2-2) 2 + 8, that is, s has the maximum value of 8
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