Answer:
a. x = 9
b. GH = 30; GK = 20
Step-by-step explanation:
An angle bisector in a triangle divides the sides proportionally.
a.
In this triangle, that means ...
(3x +3)/18 = (3x -7)/12
2(3x +3) = 3(3x -7) . . . . . . . multiply by 36
6x +6 = 9x -21 . . . . . . . . . eliminate parentheses
27 = 3x . . . . . . . . . . . . . . add 21 -6x
x = 9 . . . . . . . . . . . . . . . divide by 3
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b.
The segment lengths are found by substituting the value of 3x in each of the given expressions:
GH = 3x +3 = 27 +3 = 30
GK = 3x -7 = 27 -7 = 20
