Middle school Geometry Question

From: Herb <fuzzykyh@xxxxxxxx>
Date: Thu, 13 Dec 2007 03:59:24 -0800 (PST)

In This picture (http://home.megapass.net/~kt97885535/math2.jpg),

DE is folding line &
AB = BC = CA,
AE = 6
EC = 5
A'C = 7
Then What is the value of AD ?

sol1) Since △A'BD ∽ △ECA'
A'B : EC = BD : CA'
==> 4 : 5 = BD : 7
==> BD = 28/5
so ==> AD = 11 - BD = 27/5

sol2) Since △A'BD ∽ △ECA'
A'B : EC = A'D : EA'
==> 4 : 5 = A'D : 6
==> A'D = 24/5
==> since A'D = AD , AD = 24/5

Why the answer of sol1) does not same with sol2) ???

If someone know what is wrong, please post reply.

Thanks in advance...
.

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