Answer:
(b) x = 10.5
Explanation:
The angle bisector divides the triangle line segments proportionally.
Proportion
The proportion between corresponding line segments can be written several ways. One of them is ...
long side/long side = short side/short side
x/19.3 = 3.9/7.2
Multiplying by 19.3, we get ...
x = 19.3×3.9/7.2 ≈ 10.5 . . . units
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Additional comment
You can eliminate the incorrect answer choices simply by looking at the possible side lengths of x.
19.3 -(3.9+7.2) < x < 19.3 +(3.9+7.2) . . . . . from triangle inequality
8.2 < x < 30.4 . . . . . . . simplify
There is only one answer choice in this range: the correct one.