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

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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