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i dont have rd sharma so please solve it for me. In a trapezium ABCD, AB ll DC and DC = 2AB. EF ll AB where E and F lie on BC and AD respectively such that BE /EC = 4/3. Diagonal DB intersects EF at G . Prove that 7EF = 11AB.

i dont have rd sharma so please solve it for me.
 
In a trapezium ABCD, AB ll DC and DC = 2AB. EF ll AB where E and F lie on BC and AD respectively such that BE /EC = 4/3. Diagonal DB intersects EF at G . Prove that 7EF = 11AB.

Question Image
Grade:10

1 Answers

Arun
25763 Points
3 years ago
Dear student
given DC = 2 AB

Draw BH parallel to AD. H will be the middle point of DC as AB = DH.
Sin EF || AB,   FI = AB
The ΔBHC and ΔBIE are similar as the corresponding sides are parallel.
So  IE / HC = BE / BC
      IE = HC * BE / BC 
          = y * 4x/7x = 4 y / 7
EF = FI + IE= y + 4 y /7 = 11 y / 7
so  7 EF = 11 AB
 
Regards
Arun (askIITians forum expert)

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