做直角角C的角平分线,并交斜边AB于D
过D向两直角边做垂线,交AC于E,交BC于F
则四边形CEDF即为所示正方形
设边长为X
AE:ED=DF:FB
(120-X):X=X:(80-X)
(120-X)(80-X)=X方
120*80-200X+X方=X主方
200X=120*80
X=48