A triangle has corners points A, B, and C. Side AB has a length of $5$ $5$ . The distance between the intersection of point A's angle bisector with side BC and point B is $3$ $3$ . If side AC has a length of $4$ $4$ , what is the length of side BC?

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Answer 1 · 2017-12-21T09:54:43

Length of side BC = 5.4

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

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

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

$\frac{5}{4} = \frac{3}{D C}$ $5 / 4 = 3 / (DC)$

$D C = \frac{3 \cdot 4}{5} = 2.4$ $DC = (3*4) / 5 = 2.4$

$B C = B D + D C = 3 + 2.4 = 5.4$ $BC = BD+DC= 3+2.4 =5.4$

A triangle has corners points A, B, and C. Side AB has a length of 55 . The distance between the intersection of point A's angle bisector with side BC and point B is 33 . If side AC has a length of 44 , what is the length of side BC?