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krok68 [10]
2 years ago
9

PLEASE HELP ME THANKS SO Much

Mathematics
1 answer:
allochka39001 [22]2 years ago
8 0

9514 1404 393

Answer:

  (b)  x = 7, AB = 9, AC = 12

Step-by-step explanation:

ΔAEB ~ ΔCDB so corresponding sides are proportional.

  AB/CB = AE/CD

  (x+2)/(x -4) = 12/4

  x +2 = 3(x -4) . . . . . . multiply by x-4

  x +2 = 3x -12 . . . . . . eliminate parentheses

  14 = 2x . . . . . . . . . . . add 12-x

  7 = x . . . . . . . . . . . . . divide by 2

AB = x +2 = 7 +2 = 9

BC = x -4 = 7 -4 = 3

AC = AB +BC = 9 +3 = 12

__

In summary, ...

  x = 7, AB = 9, AC = 12 . . . . . matches the 2nd choice

_____

<em>Additional comment</em>

Please note the other choices make no sense.

  (a) AB = x +2 = -5 +2 = -3 ≠ -9

  (c) AC = 2x-2 = 2(7) -2 = 12 ≠ 9

  (d) segment lengths are never negative in a geometrical figure

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