Question

12£®ÔÚÒ»¿é¾ØÐÎABCDµÄ¿ÕµØÉÏ»®Ò»¿éËıßÐÎMNPQ½øÐÐÂÌ»¯£¬Èçͼ£¬ËıßÐεĶ¥µãÔÚ¾ØÐεıßÉÏ£¬ÇÒAN=AM=CP=CQ=x m£¬ÒÑÖª¾ØÐεıßBC=200m£¬±ßAB=a m£¬aΪ´óÓÚ200µÄ³£Êý£¬ÉèËıßÐÎMNPQµÄÃæ»ýΪsm²
£¨1£©ÇóS¹ØÓÚxµÄº¯Êý¹Øϵʽ£¬²¢Ö±½Óд³ö×Ô±äÁ¿xµÄÈ¡Öµ·¶Î§£»
£¨2£©Èôa=400£¬ÇóSµÄ×î´óÖµ£¬²¢Çó³ö´ËʱxµÄÖµ£»
£¨3£©Èôa=800£¬ÇëÖ±½Óд³öSµÄ×î´óÖµ£®

Answer 1

·ÖÎö £¨1£©¸ù¾ÝS=¾ØÐÎABCDµÄÃæ»ý-2•¡÷DMQµÄÃæ»ý-2•¡÷AMNµÄÃæ»ý¼ÆËã¼´¿É£¬¸ù¾ÝANµÄ×î´óÖµ¡¢×îСֵ¼´¿ÉÈ·¶¨×Ô±äÁ¿È¡Öµ·¶Î§£®
£¨2£©ÀûÓÃÅä·½·¨½áºÏ×Ô±äÁ¿È¡Öµ·¶Î§¼´¿É½â¾öÎÊÌ⣮
£¨3£©ÀûÓÃÅä·½·¨½áºÏ×Ô±äÁ¿È¡Öµ·¶Î§¼´¿É½â¾öÎÊÌ⣮

½â´ð ½â£º£¨1£©ÓÉÌâÒâS=200a-2•$\frac{1}{2}$x²-2•$\frac{1}{2}$£¨200-x£©£¨a-x£©
¡àS=-2x²+£¨200+a£©x£¬0£¼x¡Ü200£®
£¨2£©µ±a=400£¬S=-2x²+600x£¬
S=-2£¨x-150£©²+45000£¬
¡àµ±x=150ʱ£¬SµÄÖµ×î´ó£¬×î´óֵΪ45000ƽ·½Ã×£®
£¨3£©µ±a=800ʱ£¬S=-2x²+1000x=-2£¨x-250£©²+125000£®
¡ß0£¼x¡Ü200£¬
¡àx=200ʱ£¬S×î´óÖµ=120000ƽ·½Ã×£®

µãÆÀ ±¾Ì⿼²é¶þ´Îº¯ÊýµÄÓ¦Óá¢Åä·½·¨µÈ֪ʶ£¬½âÌâµÄ¹Ø¼üÊÇѧ»á¹¹½¨¶þ´Îº¯Êý£¬½â¾öʵ¼ÊÎÊÌâÖеÄ×îÖµÎÊÌ⣬עÒâ×Ô±äÁ¿µÄÈ¡Öµ·¶Î§£¬ÊôÓÚÖп¼³£¿¼ÌâÐÍ£®