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Please help with the problem below.

 

 Sep 6, 2020
 #1
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△ABC ~ △DBE

 

By looking at the order that the letters are given in the triangle names, we can say that

 

AC / DE   =   BC / BE

                                         Since  AC = 12  we can substitute  12  in for  AC

12 / DE   =   BC / BE

                                         Since  DE = 4  we can substitute  4  in for  DE

12 / 4   =   BC / BE

                                         Since  BE = x  we can substitute  x  in for  BE

12 / 4   =   BC / x

                                         Since  BC  =  BE + EC  we can substitute  BE + EC  in for  BC

12 / 4   =   (BE + EC) / x

                                         Since  BE = x  we can substitute  x  in for  BE, and since  EC = 6  we can substitute  6  in for  EC

12 / 4   =   (x + 6) / x

                                         Now we just have to solve this equation for  x. First let's simplify  12 / 4

3   =   (x + 6) / x

                                         Multiply both sides of the equation by  x

3x   =   x + 6

                                         Subtract  x  from both sides of the equation

3x - x  =  6

                                         3 apples - 1 apple = 2 apples, so  3x - x = 2x

2x   =   6

                                         Divide both sides by  2

x   =   3

 Sep 6, 2020

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