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Triangle ABC is similar to triangle DEF. The length of AC---- is 12 cm. The length of EF--- is 15 cm. The length of DF---- is 9cm.

What is the length of BC----?

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JonHenderson55
Answer:  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)"   ;    { b[tex] \neq [/tex]0 ; d[tex] \neq [/tex]0 } ;

           " 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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Answer:  The length of BC is:  " 20 cm " .
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The triangle ABC and triangle DEF are similar so the value of the length of BC is 20 cm and this can be determined by using the properties of a similar triangle.

Given :

  • Triangle ABC is similar to triangle DEF.
  • The length of AC is 12 cm.
  • The length of EF is 15 cm.
  • The length of DF is 9cm.

The following steps can be used to determine the length of BC:

Step 1 - According to the given data, triangle ABC is similar to triangle DEF.

Step 2 - So, according to step 1:

[tex]\rm \dfrac{AC}{DF} = \dfrac{BC}{EF}[/tex]

Step 3 - Substitute the values of length AC, DF, and EF in the above equation.

[tex]\rm \dfrac{12}{9} = \dfrac{BC}{15}[/tex]

Step 4 - Multiply 15 on both sides in the above expression.

[tex]\rm \dfrac{12}{9}\times 15 = BC[/tex]

Step 5 - Simplify the above expression in order to get the value of the length BC.

BC = 20 cm

For more information, refer to the link given below:

https://brainly.com/question/19237987

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