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Geometry: Find x AB*AC=AD*AE

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Mar 16th, 2015

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

Mar 16th, 2015

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