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
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In summary, ...
x = 7, AB = 9, AC = 12 . . . . . matches the 2nd choice
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Additional comment
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
