Rectangle ABCD, e and F are on BC and CD respectively. The area of triangle Abe, CEF and ADF are 2, 3 and 4 respectively

Analysis: if AB = x, CE = y, the values of CF, DF and ad can be calculated, and CD = CF + FD, the area of rectangular ABCD can be calculated according to AD and CD, and the area of △ AEF can be calculated according to s △ AEF = s rectangular abcd-s △ abe-s △ cef-s △ ADF
Let AB = x, CE = y
∵∠ B = ∠ C = 90 ° and s △ Abe = 2,
So 12 &; be &; X = 2, that is be = 4 / X
Similarly, CF = 6 / y
So DF = cd-cf = ab-cf = X-6 / y,
AD= 8DF= 8/(x-6/y)．
And ad = BC,
That is 8 / (x-6y) = 4 / x + y
It is reduced to (XY) &# 178; - 10xy-24 = 0
The solution is xy = 12,
The area of rectangle ABCD = x (4 / x + y) = 4 + xy = 16,
S △ AEF = s rectangle abcd-s △ abe-s △ cef-s △ ADF = 7,
So the answer is 7

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