点C、D在直线AB上,线段AC,CB,AD,DB的长度满足.点C,D在直线AB上,线段AC,CB,AD,DB的长度满足AC:CB=5:4,AD:DB=2:1,且CD=2cm,求线段AB的长.四种答案都要,
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点C、D在直线AB上,线段AC,CB,AD,DB的长度满足.点C,D在直线AB上,线段AC,CB,AD,DB的长度满足AC:CB=5:4,AD:DB=2:1,且CD=2cm,求线段AB的长.四种答案都要,
点C、D在直线AB上,线段AC,CB,AD,DB的长度满足.
点C,D在直线AB上,线段AC,CB,AD,DB的长度满足AC:CB=5:4,AD:DB=2:1,且CD=2cm,求线段AB的长.四种答案都要,
点C、D在直线AB上,线段AC,CB,AD,DB的长度满足.点C,D在直线AB上,线段AC,CB,AD,DB的长度满足AC:CB=5:4,AD:DB=2:1,且CD=2cm,求线段AB的长.四种答案都要,
设AB长为 x cm
第一种情况:
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A C D B
AC = 5/(5+4) AB = 5/9 AB
AD = 2/(2+1) AB = 2/3 AB
CD= AD - AC = (2/3-5/9) AB= 1/9 AB= 2
AB=18 cm
第二种情况:
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A D B C
AD = 2/3 AB (同第一种情况)
AC = (5/(5-4) AB =5AB
CD= AC-AD =(5 - 2/3)AB=13/3 AB =2
AB= 6/13 cm
第三种情况:
---------------------------------------------------------------
A C B D
AC= 5/9 AB (同第一种情况)
AD= 2/(2-1) AB =2AB
CD =AD-AC = (2-5/9) AB= 13/9 AB=2
AB=18/13 cm
第四种情况:
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A B D C
AC = 5AB (同第二种情况)
AD = 2AB(同第三种情况)
CD = AC - AD = 3AB =2
AB= 2/3 cm
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