Given that the common parts of AB and CD BD = 1 / 3AB = 1 / 7CD, e and F are the midpoint of AB and CD respectively, and the distance of EF is 6cm, find the length of AB and CD
A——E——D——B——F——C
∵BD=1/3AB
∴AB=3BD
∵ e is the midpoint of ab
∴BE=AB/2=3/2BD
∵BD=1/7CD
∴CD=7BD
∵ f is the midpoint of CD
∴DF=7/2BD
∴BF=DF-BD=7/2BD-BD=5/2BD
∴EF=BE+BF=3/2BD+5/2BD=4BD
∵EF=6
∴4BD=6
∴BD=1.5
∴AB=3BD=4.5(cm)
∴CD=7BD=10.5(cm)
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