A triangle has corners points A, B, and C. Side AB has a length of $15$ $15$ . The distance between the intersection of point A's angle bisector with side BC and point B is $4$ $4$ . If side AC has a length of $18$ $18$ , what is the length of side BC?

Question

2531 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-21T09:18:34

Length of BC = 8.8

Let the point where the angle bisector intersects with
side BC be D

$using the angle bisector theorem$ $"using the "color(blue)"angle bisector theorem"$

$\frac{A B}{A C} = \frac{B D}{D C}$ $(AB)/(AC)=(BD)/(DC)$

$\frac{15}{18} = \frac{4}{D C}$ $15 / 18 = 4 / (DC)$

$D C = \frac{4 \cdot 18}{15} = 4.8$ $DC = (4*18) / 15 = 4.8$

$B C = B D + D C = 4 + 4.8 = 8.8$ $BC = BD+DC= 4+4.8 =8.8$

A triangle has corners points A, B, and C. Side AB has a length of 15 1515 . The distance between the intersection of point A's angle bisector with side BC and point B is 4 44 . If side AC has a length of 18 1818 , what is the length of side BC?