已知三角形abc三边长为a,b,c满足a+b+c=9,a^2+b^2+c^2=27,则三角形abc的面积为()
问题描述:
已知三角形abc三边长为a,b,c满足a+b+c=9,a^2+b^2+c^2=27,则三角形abc的面积为()
答
∵(a+b+c)²=a²+b²+c²+2ab+2ac+2bc=27+2ab+2ac+2bc=81∴ab+ac+bc=27∵2a²+2b²+2c²-2ab-2ac-2bc=2*27-2*27=0∴(a²-2ab+b²)+(a²-2ac+c²)+(b²-2bc+c²...