见图片解答
设门宽为x则半圆面积为：S1=0.5*π*（x/2）^2=（πx^2）/8∴矩形面积S2=5-（πx^2）/8∴矩形高h=[5-（πx^2）/8]/x门框周长l=0.5*πx+2*[5-（πx^2）/8]/x+x=（π/4+1）x+10/xdl/dx=π/4+1-10/(x^2)令=0得x=40/（π+4）即门宽为40/（π+4）时周长最短
