如图所示,△ABC中,|AB|=2,|BC|=3.3个红色三角形面积之和即为所求.
S△ADE=(1/2)|AE|*|AD|*sin∠DAE=|AC|sin∠CAB
S△BFG=(1/2)|BF|*|BG|*sin∠FBG=3sin∠ABC
S△CHI=(1/2)|CH|*|CI|*sin∠HCI=(3/2)|AC|sin∠BCA
在△ABC中,由正弦定理有:|AC|/sin∠ABC=3/sin∠CAB=2/sin∠BCA
故3个三角形面积之和=|AC|sin∠CAB+3sin∠ABC+(3/2)|AC|sin∠BCA=3*3sin∠ABC≤9*1=9
当且仅当∠ABC=90°时取“=”.
![](http://c.hiphotos.baidu.com/zhidao/wh%3D600%2C800/sign=e35513aa277f9e2f7060150e2f00c51c/d31b0ef41bd5ad6e9f1ac5a681cb39dbb7fd3c9e.jpg)