Question

Jamal drew angle bisector AD with D on the line segment BC. If BD=3, DC=9 and AB+AC=28 find AB and AC.

Answer 1

Answer:

  AB = 7

  AC = 21

Step-by-step explanation:

Because AD is an angle bisector it divides the triangle into proportional parts. That is ...

  AC/DC = AB/BD

  (28 -AB)/9 = AB/3 . . . . use AC = 28 -AB

  28 -AB = 3AB . . . . . . . . multiply by 9

  28 = 4AB . . . . . . . . add AB

  AB = 28/4 = 7 . . . . divide by 4

  AC = 28 -7 = 21

The lengths AB and AC are 7 and 21, respectively.

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Additional comment

The triangle ABC cannot exist. The reason is that its side measures are 7, 12, and 21. The sum of 7 and 12 is not greater than 21, so the side measures do not satisfy the triangle inequality.

For the triangle to exist, the sum of AB and AC cannot exceed 24 for the given values of BD and DC.