??

[knotty epoch]

,rccw

[wild beacon]

Hint: Note that triangles ABD and ADC have the same height AB. What does this allow you to say about their bases?

[sterile gate]

I have just tried my best
Here we go
CD=8-BD
Area Ratio --> 1/2AB.BD÷1/2 AB(8-BD)=3÷5
AB.BD÷AB(8-BD)=6÷10
AB.BD=6
AB(8-BD)=10
8AB-AB.BD=10
8AB-6=10
8AB=16
AB=2
BD=6/2=3
Since there is no answer we can increase ratio by multiplication of 2
AB.BD=6×2=12
Factor of 12 --> 1, 2, 3, 4, 6,12
Check if area ratio =3÷5
If BD=2 and AB=6
2×6/2÷(8-2)×6/2=3÷5
6÷18=3÷5
3÷9=/=3÷5; so this is not the answer
The rest of factor is ignored since there is no right option
Since there is no answer we can increase ratio by multiplication of 2
So AB.BD=12×2=24
Factor of 24 is=1, 2, 3, 4, 6, 8, 12, 24
Check if area ratio=3÷5
If BD=3 and AB=8
3×8/2÷(8-3)×8/2=3÷5
12÷20=3÷5
3÷5=3÷5
So we got the answer
AB=8