长方形ABCD的周长为16米,在它的每条边上各画一个以该边为边的正方形(如图),已知这四个正方形的和是68 如图,长方形ABCD的周长为16米,在它的每条边上各向外画一...
\u957f\u65b9\u5f62ABCD\u7684\u5468\u957f\u4e3a16\u7c73\uff0c\u5728\u5b83\u7684\u6bcf\u6761\u8fb9\u4e0a\u5404\u753b\u4e00\u4e2a\u4ee5\u8be5\u8fb9\u4e3a\u8fb9\u7684\u6b63\u65b9\u5f62\uff08\u5982\u56fe\uff09\uff0c\u5df2\u77e5\u8fd9\u56db\u4e2a\u6b63\u65b9\u5f62\u7684\u548c\u662f68\u8bbe\u957f\u65b9\u5f62ABCD\u7684\u957f\u548c\u5bbd\u5206\u522b\u662fa\u548cb\uff0c\u6839\u636e\u9898\u610f\u5f97a 2 +a 2 +b 2 +b 2 =68\uff0c2\uff08a 2 +b 2 \uff09=68\uff0ca 2 +b 2 =34\uff0c\uff08a+b\uff09 2 -2ab=34\uff0c\u56e0\u957f\u65b9\u5f62\u7684\u5468\u957f\u662f16\u7c73\uff0c\u6240\u4ee5a+b=16\u00f72=8\uff08\u7c73\uff09\uff0c\uff08a+b\uff09 2 -2ab=34\uff0c 8 2 -2ab=34\uff0c 64-34=2ab\uff0c ab=30\u00f72\uff0c ab=15\uff08\u5e73\u65b9\u7c73\uff09\uff0e\u7b54\uff1a\u957f\u65b9\u5f62ABCD\u7684\u9762\u79ef\u662f15\u5e73\u65b9\u7c73\uff0e\u6545\u7b54\u6848\u4e3a\uff1a15\uff0e
\u8bbe\u957f\u65b9\u5f62\u7684\u957f\u4e3ax\uff0c\u5bbd\u4e3ay
2x²+2y²=68
x²+y²=34\u2460
\u2235x+y=16
(x+y)²=16²
x²+2xy+y²=256\u2461
\u2461-\u2460
2xy=222
xy=111
\u957f\u65b9\u5f62\u9762\u79ef\u662f111
a2+a2+b2+b2=68,
2(a2+b2)=68,
a2+b2=34,
(a+b)2-2ab=34,
因长方形的周长是16米,
所以a+b=16÷2=8(米),
(a+b)2-2ab=34,
82-2ab=34,
64-34=2ab,
ab=30÷2,
ab=15(平方米).
答:长方形ABCD的面积是15平方米.
故答案为:15.
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