Triangle abc is similar to triangle def. the length of is 12 cm. the length of is 15 cm. the length of is 9cm. what is the length of enter your answer in the box cm

 The length of BC is:  " 20 cm " .
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Explanation:
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[AC] / [DF]  = 12 cm / 9 cm ;

[BC] / [EF] =        x  /  15 cm ; 

12 / 9 = x / 15 ;  Solve for "x" ;   {Note:  "x" is the length of BC (in cm) ;

Simplify   the " (12/9) " ; 

→  " 12 / 9  = (12 ÷ 3) / (9 ÷ 3) " ;

 = 4 / 3 ;

And rewrite:  

→  4 / 3  = x / 15 ;   Solve for "x" ;
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Note:  Cross-multiply:

Given:  "(a/b)" = (c/d)"   ;    { b0 ; d0 } ;

           " a*d = b*c " .
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As such:
 
→  3x = 15 * 4 ; 

→  3x = 60 ;  
 
Divide EACH SIDE of the equation by "3" ; 
   to isolate "x" on one side of the equation;  & to solve for "x" ; 
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→  3x / 3 = 60 / 3 ; 

→  x = 20 .
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 The length of BC is:  " 20 cm " .
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45x is the correct answer

Horizontal change or the change of x