Steps of construction
1. Draw a line segment AB = 7 cm
2. Draw a ray AX, making acute ∠BAX
3. Along AX mark 3 + 5 = 8 Points
A1,A2,A3,A4,A5,A6,A7,A8such that
AA1=AA2=A2A3=A3A4=A4A5=A5A6=A6A7=A7A8
4. Join A8B
5. From A3. Draw A3C||A8B meeting AB at C.
[By making an angle equal to ∠BA8A at A3]
Then C is the point on AB which divides it in the ratio 3:5.
Thus AC : BC = 3 : 5
Justification
Let AA1=A1A2=A2A4=A7A8=x
In ΔABA8, we have A3C||A8B
∴ACCB=AA3A3A8=3X5X=35
Hence AC : CB = 3 : 5