Question

如图,矩形ABCD的四个顶点在正三角形EFG的边上,已知△EFG的边长为2,记矩形ABCD的面积为S,边长AB为x,则S

Answer 1

作△EFG的高EH交矩形ABCD的边AD于点M,于是MH是矩形ABCD的高,

则EH=√3,EM=√3/2*x,MH=√3-√3/2*x,

矩形面积=AB*MH,即

S=x(√3-√3/2*x),即S=-√3/2*x^2+√3*x (0