设扇形的半径是r,则扇形的弧长是(p-2r)
扇形的面积=(p-2r)×r×1/2
=-r²+(p/2)r
=-[r²-(p/2)r]
=-[r²-(p/2)r+(p/4)²]+(p/4)²
=-[r-(p/4)]²+p²/16
当扇形的半径r=p/4时,扇形面积有最大值,最大值是p²/16
设扇形的半径是r,则扇形的弧长是(p-2r)
扇形的面积=(p-2r)×r×1/2
=-r²+(p/2)r
=-[r²-(p/2)r]
=-[r²-(p/2)r+(p/4)²]+(p/4)²
=-[r-(p/4)]²+p²/16
当扇形的半径r=p/4时,扇形面积有最大值,最大值是p²/16