In triangle $abc$, $ab = 16$, $ac = 24$, $bc = 19$, and $ad$ is an angle bisector. find the ratio of the area of triangle $abd$ to the area of triangle $acd$. (express your answer as a fraction in lowest terms.)'

Explanation:

We have triagle ABC bisected by angle AD, like is shown in the image.

A bisector angle is a line which cuts an angle into two equal halves.

So:

BC = BD + DC ∴ 19  =BD + DC ⇒ BD = 19 - DC  (1) because D cuts BC in 2 parts.

By angle bisector theorem: the ratio of any 2 sides of a triagle is equal to the ratio of the lenths formed on its third side by the anfle bisectorof the anfle formed by those 2 sides:

(2) read: side AB is BD as AC is to DC

Clear DC:

(3)

we know: AC = 24, BD = 19 - DC (from (1)) and AB = 16

replacing all the values:

(4)

for (4) in (1)

BD = 19 - = (5)

the answer is b hope you pass

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