Question

已知三角形ABC的三边的长分别为m^2-n^2,2mn,m^2+n^2,判断三角形的形状.

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已知三角形ABC的三边的长分别为m^2-n^2,2mn,m^2+n^2,判断三角形的形状.

Answer 1

a=m^2+n^2
b=m^2-n^2
c=2mn
b^+c^2=(m^2-n^2)^2+(2mn)^2
=m^4-2m^2*n^2+n^4+4m^2*n^2
=m^4+2m^2*n^2+n^4=(m^2+n^2)=a^2
即：b^2+c^2=a^2
所以三角形ABC为直角三角形

Answer 2

∵(m^2-n^2)^2+(2mn)^2
=m^4-2m^2*n^2+n^4+4m^2*n^2
=m^4+2m^2*n^2+n^4
=(m^2+n^2)^2
∴三角形为直角三角形