### [數學]正三角形面積的最小值

#ed_op#DIV#ed_cl#感謝#ed_op#SPAN class=name#ed_cl##ed_op#A name=""#ed_cl##ed_op#/A#ed_cl##ed_op#B#ed_cl##ed_op#SPAN class=name#ed_cl##ed_op#A name=""#ed_cl##ed_op#/A#ed_cl##ed_op#B#ed_cl##ed_op#SPAN class=name#ed_cl##ed_op#A name=""#ed_cl##ed_op#/A#ed_cl##ed_op#B#ed_cl##ed_op#FONT size=2#ed_cl#aaddfg、#ed_op#/FONT#ed_cl##ed_op#/B#ed_cl##ed_op#/SPAN#ed_cl##ed_op#FONT size=2#ed_cl#宇智波鼬、#ed_op#/FONT#ed_cl##ed_op#/B#ed_cl##ed_op#/SPAN#ed_cl##ed_op#FONT size=2#ed_cl#☆ ~ 幻 星 ~ ☆#ed_op#/FONT#ed_cl##ed_op#/B#ed_cl##ed_op#/SPAN#ed_cl#三位大大的解答#ed_op#/DIV#ed_cl#

=1/2*k*(a-3k)*sin60度+1/2*2k*(a-k)sin60度+1/2*3k*(a-3k)sin60度
=根號3/4*k(6a-11k)
=11*根號3/4*(6/11*k*a-k^2)
=-11*根號3/4*(k-3/11*a)^2+9根號3/44*a^2
k=3a/11時外面三角形面積和有最大值
CR=3k=9a/11

#ed_op#DIV#ed_cl#9a/11應該是對的...我也是這個答案#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#&nbsp;#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#設AP=k,BQ=2k,CR=3k#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#ΔAPR : ΔABC=ak-k#ed_op#SUP#ed_cl#2 #ed_op#/SUP#ed_cl#: a#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#ΔBQR :&nbsp;ΔBCA=2ak-2k#ed_op#SUP#ed_cl#2 #ed_op#/SUP#ed_cl#: a#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#ΔCRQ : ΔCAB=3ak-3k#ed_op#SUP#ed_cl#2 #ed_op#/SUP#ed_cl#:&nbsp;a#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#(頂角相同,三角形面積比=夾邊乘積比)#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#ΔPQR : ΔABC=(√3)/4*(a#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#-6ak+11k#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#) : (√3)/4*a#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#ΔPQR=(11√3)/4*(k#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#-6a/11+9a#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#/121)-9a#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#/121*(11√3)/4+(√3)/4*a#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#SUP#ed_cl#&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; #ed_op#/SUP#ed_cl#=(11√3)/4*(k-3a/11)#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#+√3a#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#/22≥√3a#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#/22#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#意謂當k=3a/11時有最小值√3a#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#/22#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#此時CR=9a/11#ed_op#/DIV#ed_cl#

### [數學]正三角形面積的最小值

#ed_op#DIV#ed_cl#此題好難請大大幫忙解一下謝謝#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#IMG height=132 alt="image file name: 2k2aad1cc0e2.jpg" src="http://yll.loxa.edu.tw/phpBB2/richedit/upload/2k2aad1cc0e2.jpg" width=585 border=0#ed_cl##ed_op#/DIV#ed_cl#