满足1:2:3,设AD=x,试求三角形DEF的面积y关于x的函数.
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S△ADF=1/2*sin60*AD*AF=1/2*sin60*x*(a-3x)同理S△BDE=1/2*sin60*2x*(a-x)S△CFE=1/2*sin60*3x*(a-2x)相加得√3/2(3ax-6x^2)则S△DEF=S△ABC-√3/2(3ax-6x^2)=(√3/4)a^2-√3/2(3ax-6x^2)=√3/4(a^2-6ax+12x^2) (0
满足1:2:3,设AD=x,试求三角形DEF的面积y关于x的函数.
S△ADF=1/2*sin60*AD*AF=1/2*sin60*x*(a-3x)同理S△BDE=1/2*sin60*2x*(a-x)S△CFE=1/2*sin60*3x*(a-2x)相加得√3/2(3ax-6x^2)则S△DEF=S△ABC-√3/2(3ax-6x^2)=(√3/4)a^2-√3/2(3ax-6x^2)=√3/4(a^2-6ax+12x^2) (0