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 AB is 10 inches? Express your answer as a common fraction.
+204 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
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