Why are triangles always named ABC?

Geometry Level 3

The angle bisector at vertex A of △ A B C \bigtriangleup ABC meets BC at point D. If AB = 30, AC = 24 and BC = 36, find BD.


The answer is 20.

Hillary Diane Andales by Hillary Diane Andales , 21, USA

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1 solution

Let's use the Angle Bisector theorem, which says that if A D AD is the angle bisector of ∠ A \angle A in triangle △ A B C \triangle ABC , then:

A B B D = A C C D \dfrac{AB}{BD}=\dfrac{AC}{CD}

Let B D = x BD=x , hence C D = 36 − x CD=36-x . So:

30 x = 24 36 − x \dfrac{30}{x}=\dfrac{24}{36-x}

Solving for x x we get B D = 20 BD=\boxed{20} .

3 Helpful 0 Interesting 0 Brilliant 0 Confused

brother ...... if AB/BD = AC/CD ....... then AB/AC = BD/CD ........ so u get the ratio of the 2 parts ..... i think this is easier than cross multiplying and solving for "x"

Ganesh Ayyappan - 6 years, 5 months ago

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