设三边长为a,b,c(斜边),则a^2+b^2=c^2
因为a+b+c=L=a+b+(a^2+b^2)^(1/2)≥2(ab)^(1/2)+(2ab)^(1/2)=(2+√2)(ab)^(1/2)
所以ab≤[(3-2√2)/2]*L^2
S=ab/2最大值为[(3-2√2)/4]*L^2