1.若三角形ABC的三边a.b.c满足,a^2+b^2+c^2=10a+24b+26c,求三角形ABC的面积2.如图,三角形ABC中,AB大于AC,AD为中线,AC为高,求证AB^2-AC^2=2BC*DE
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![1.若三角形ABC的三边a.b.c满足,a^2+b^2+c^2=10a+24b+26c,求三角形ABC的面积2.如图,三角形ABC中,AB大于AC,AD为中线,AC为高,求证AB^2-AC^2=2BC*DE](/uploads/image/z/1602846-54-6.jpg?t=1.%E8%8B%A5%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E7%9A%84%E4%B8%89%E8%BE%B9a.b.c%E6%BB%A1%E8%B6%B3%2Ca%5E2%2Bb%5E2%2Bc%5E2%3D10a%2B24b%2B26c%2C%E6%B1%82%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E7%9A%84%E9%9D%A2%E7%A7%AF2.%E5%A6%82%E5%9B%BE%2C%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E4%B8%AD%2CAB%E5%A4%A7%E4%BA%8EAC%2CAD%E4%B8%BA%E4%B8%AD%E7%BA%BF%2CAC%E4%B8%BA%E9%AB%98%2C%E6%B1%82%E8%AF%81AB%5E2-AC%5E2%3D2BC%2ADE)
1.若三角形ABC的三边a.b.c满足,a^2+b^2+c^2=10a+24b+26c,求三角形ABC的面积2.如图,三角形ABC中,AB大于AC,AD为中线,AC为高,求证AB^2-AC^2=2BC*DE
1.若三角形ABC的三边a.b.c满足,a^2+b^2+c^2=10a+24b+26c,求三角形ABC的面积
2.如图,三角形ABC中,AB大于AC,AD为中线,AC为高,求证AB^2-AC^2=2BC*DE
1.若三角形ABC的三边a.b.c满足,a^2+b^2+c^2=10a+24b+26c,求三角形ABC的面积2.如图,三角形ABC中,AB大于AC,AD为中线,AC为高,求证AB^2-AC^2=2BC*DE
1.若三角形ABC的三边a.b.c满足,a²+b²+c²=10a+24b+26c,求三角形ABC的面积
应该是a²+b²+c²+338=10a+24b+26c吧?
因为a²+b²+c²+338=10a+24b+26c
故:a²+b²+c²+338-10a-24b-26c=0
故:a²-10a +25+b²-24b +144+c²-26c +169=0
故:(a-5)²+(b-12) ²+(c-13) ²=0
故:a=5,b=12,c=13
因为a²+b²=c²
故:△ABC是Rt△
故:△ABC的面积S=1/2•ab=30
2.如图,三角形ABC中,AB大于AC,AD为中线,AE为高,求证AB²-AC²=2BC*DE
因为AD为中线,故:BD=CD
因为AE为高
故:
在Rt△ABE中,AB²=BE²+AE²
在Rt△ACE中,AC²=CE²+AE²
故:AB²-AC²=BE²-CE²
=(BE+CE)(BE-CE)
=BC*[BD+DE-(CD-DE)]
= BC*(BD-CD+2DE)
=2BC*DE