设长方形长为a,宽为b,则2(a+b)=120a+b=601.ab=500==>a(60-a)=500==>a^2-60a+500=0==>(a-10)(a-50)=0,所以a=10,b=50或a=50,b=102.ab=675==>a(60-a)=675==>a^2-60a+675=0==>(a-25)(a-35)=0,所以a=25,b=35或a=35,b=253....ab<=1/4*(a+b)^2=1/4*60^2=900这步没看懂，麻烦解说一下(a-b)^2=a^2+b^2-2ab=a^2+b^2+2ab-4ab=(a+b)^2-4ab>=0所以4ab<=(a+b)^2ab<=1/4*(a+b)^2