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Can someone help  △EDC is similar to △ABC. Solve for x.

 

 

 

△ABC is similar to △DEF.

 Sep 9, 2018
 #1
avatar+7352 
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△EDC  is similar to  △ABC ,  so side  DC  corresponds to side  BC .

 

Let the scale factor from  △EDC  to  △ABC  be  s .

 

DC * s   =   BC

 

4 * s   =   6

 

s   =   6/4

 

s   =   1.5

 

So each side of  △ABC  is  1.5  times the corresponding side of  △EDC.

 

EDC  is similar to  △ABC ,  so side  EC  corresponds to side  AC .

 

EC * 1.5   =   AC

 

And we can see from the picture that   EC  =  x   and   AC  =  12.5 - x  , so....

 

x * 1.5   =   12.5 - x

 

1.5x   =   12.5 - x

                                 Add  x  to both sides of the equation.

1.5x + x   =   12.5

 

2.5x   =   12.5

                                 Divide both sides by  2.5 .

x   =   5

 Sep 10, 2018
 #2
avatar+7352 
0

The sum of the angles in every triangle is  180° , so..

 

∠A + ∠B + ∠C   =   180°

 

21° + 90° + ∠C   =   180°

 

∠C   =   180° - 21° - 90°

 

∠C   =  69°

 

∠D  corresponds to  ∠A  so...

 

∠D   =   ∠A   =   21°

 

∠F  corresponds to  ∠C  so...

 

∠F  =  ∠C  =  69°

 Sep 10, 2018

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