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As shown in the figure, in rectangle ABCD, ab = 2ad, line EF = 10. Take a point m on EF, and make rectangle emnh and rectangle mfgn with EM and MF as sides respectively, so that rectangle mfgn ∽ rectangle ABCD. Let Mn = x, when x is the value, the area s of rectangle emnh has the maximum value. What is the maximum value?
∵ rectangle mfgn ∵ rectangle ABCD, ∵ mnad = mfab. (1 point) ∵ AB = 2ad, Mn = x, ∵ MF = 2x. (2 points) ∵ EM = ef-mf = 10-2x (0 ＜ x ＜ 5) ∵ s = x (10-2x) (5 points) = - 2x2 + 10x = - 2 (X-52) 2 + 252. ∵ when x = 52, the maximum value of S is 252. (8 points)
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