A triangle has corners points A, B, and C. Side AB has a length of 9 9. The distance between the intersection of point A's angle bisector with side BC and point B is 8 8. If side AC has a length of 14 14, what is the length of side BC?

1 Answer
Jun 21, 2017

BC=20 4/9BC=2049

Explanation:

"let the point where the angle bisector intersects with side"let the point where the angle bisector intersects with side
"BC be D"BC be D

"then using the "color(blue)"Angle bisector theorem"then using the Angle bisector theorem

color(red)(bar(ul(|color(white)(2/2)color(black)((AB)/(AC)=(BD)/(DC))color(white)(2/2)|)))

"require to find DC"

rArr9/14=8/(DC)

rArr9DC=14xx8larrcolor(blue)" cross-multiplying"

rArrDC=(14xx8)/9=112/9

rArrBC=BD+DC=8+112/9=184/9=20 4/9

BC=20 4/9larrcolor(red)" exact value"