2019 Mock AMC 10B Problems/Problem 15
The area of the larger square is 144, so each side length is 12. m + n = 12. Also, Each of the smaller 4 triangles are right triangles, so m²+n²= 108.
n=12-m m²+(12-m)²=108 m²+144-24m+m²=108.
Solving for m gives m= 12+sqrt(72)/2, m = 6+3sqrt2, a=6, b=3, c=2. a+b+c=11. (A)