Answer:
x = 5
Explanation:
The sum of the side lengths shown is ...
(2x) + (3x +2) + (4x +1) = 9x +3
That is the perimeter of the inscribed triangle. That triangle is similar to triangle ABC by a scale factor of 1:2, so the perimeter of ΔABC is ...
2(9x +3) = 96 = 18x +6
90 = 18x . . . . subtract 6
90/18 = x = 5 . . . . . divide by the coefficient of x