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.





Here's a "mock"  pic




    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



cool cool cool

CPhill  Mar 1, 2018

Thanks so much!

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