The electric field at point $$p$$ due to an electric dipole is $$E$$. The electric field at point $$R$$ on equitorial line will be $$\frac{E}{x}$$. The value of $$x$$ 

Dipole moment magnitude:

$$p=q(2r)=2qr$$

At point P on axial line, distance from center is

$$OP=r$$

Axial field of dipole:

$$E_P=\frac{2kp}{r^3}$$

Given this is

E

so

$$E=\frac{2kp}{r^3}$$

Now point R lies on equatorial line at distance

OR=2r

Equatorial field of dipole:

Then

$$E_R=\frac{kp}{(2r)^3}$$

$$=\frac{kp}{8r^3}$$

Using

$$E=\frac{2kp}{r^3}$$

we get

$$E_R=\frac{1}{16}E$$

So

$$\frac{E}{x}=\frac{E}{16}$$