As shown in the figure, the common part of line AB and CD is BD, and BD = 1 / 4AB = 1 / 5CD, e and F are the midpoint of AB and CD respectively, EF = 7cm, find the length of AB and CD

As shown in the figure, the common part of line AB and CD is BD, and BD = 1 / 4AB = 1 / 5CD, e and F are the midpoint of AB and CD respectively, EF = 7cm, find the length of AB and CD

Let BD = k, then AB = 4K, CD = 5K
Because e and F are the midpoint of AB and CD respectively, EB = AB / 2 = 4K / 2 = 2K, DF = CD / 2 = 5K / 2 = 2.5k
According to the graph:
ED=EB-BD=2k-k=k,BF=DF-BD=2.5k-k=1.5k
So EF = ed + BD + BF = K + K + 1.5k = 3.5K
Because EF = 7cm, so 3.5K = 7cm, k = 2cm
So AB = 4K = 8cm, CD = 5K = 10cm