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# 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

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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!

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#1
+83944
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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

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
#2
+769
+1

Thanks so much!

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