在直角三角形abc中,角C等于90°,cd是ab边上的高,若ac=8,bd=2求cd

在直角三角形abc中,角C等于90°,cd是ab边上的高,若ac=8,bd=2求cd
在直角三角形abc中,角C等于90°,cd是ab边上的高
,若ac=8,bd=2求cd

在直角三角形abc中,角C等于90°,cd是ab边上的高,若ac=8,bd=2求cd
设BC=x,则CD=√(x²-4),AB=√(x²+64)
8x=√(x²+64)*√(x²-4)=√[(x²+64)(x²-4)]
64x²=(x²+64)(x²-4)
x^4-4x²-256=0
(x²-16)(x²+8)=0
x²-16=0
x>0
x=4
CD=√(x²-4)=2√3

设cd=x 则bc=x2+4开根号，相似三角形可得x/2=8/bc 两边平方可得(x2+2)的平方=256，可得x=2根号3

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