Answer:
see below & attached
Explanation:
red line length call it a² = (8√3)²- 12² = 192-144 =48
so look at the graph we know x is longer than 12,
the portion that's longer than 12 call it c = x-12
top short line call it b
because it's all right angle you are looking at 3 right angle triangles
the big one that's cut into 2 by the red line
the larger one & the smaller one
each will have this property: short side 1 ²+short side 2 ²= long side ²
so for the largest one:
(8√3)² +b² = (12+c)² = x²
second largest triangle we already know all 3 sides: (8√3), 12, √48
now look at the smallest
48+c² =b²
once you have all equations listed , you can solve for c.
see attached.