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Points F, E, D are on the sides AB, AC, and BC , respectively, of right triangle ABC such that AFDE is a square. If AB = 12 and AC = 18, then what is AF?

 

 Feb 10, 2022
 #1
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Note that triangles  BAC  and BFD  are similar

 

Since AB = 12, let the side of the square  = x =  AF

 

Then BF  =  12  - x      ....and  by similar  triangles we  have that

 

AB / FB  =  AC / DF

 

12 / ( 12- x)  =  18 / x            .....cross-multiply

 

12x  =  ( 12 - x ) 18

 

12x = 216 - 18x        ......  add 18x to both sides

 

30x =  216               .......divide both sides by 30

 

x = 216 / 30   =  7.2 =  AF

 Feb 10, 2022

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