尝试另一个解法

Draw a perpendicular line, a being the upper section, b the lower section. It also divides the 19 triangle into two areas, x and y.

(a/b)^2=x/8=y/12=(x+y)/(8+12)=19/20

let rectangle area be S.

19*2/S=a/b=sqrt(19/20)

S=4*sqrt(95)