as

AB * AC = AD * AE

then

AB = 15 AC = 32

AD = x AE = x + 14

Now

15 * 32 = x * (x +14)

480 = x^2 + 14x

x^2 + 14x - 480 = 0

x^2 + 30x - 16x - 480 = 0

x(x + 30) - 16(x - 30) = 0

(x - 16)(x + 30) = 0

x = 16 or x = - 30

As length cannot be negative, then

we neglect x = - 30

So x = 16

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