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

 Dec 16, 2021
 #1
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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 

 

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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 Dec 16, 2021
 #2
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Side AB = 10       ( not 15 )

 

AC = 2/3(AB)

 

BC = 4/3(10)

 

AD = 2 18/21

 

DC = 3 17/21

Guest Dec 17, 2021

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