The sides of triangle CAB are in the ratio of 2:3:4. Segment BD is the angle bisector drawn to the shortest side, dividing it into segments AD and DC. What is the length, in inches, of the longer subsegment of side AC if the length of side AC is 10 inches? Express your answer as a common fraction.

Thanks!

AnonymousConfusedGuy
Mar 1, 2018

#1**+1 **

Here's a "mock" pic

C

10 20

A 15 B

Side AB = 15......side BC = 20

If B is bisected....we have this ratio

BC / AB = longer segment DC / shorter segment AD

20/15 = DC / AD

4/3 = DC / AD

Thus.......AC is split into 7 equal parts...and DC is 4 of these....so its length is

(4/7) * 10 = 40 / 7 units

CPhill
Mar 1, 2018