A wire of resistance R is bent to form a square A B C D as shown in the figure. The effective resistance…

If the resistance of the wire is R, then each arm of the square has a resistance of $\frac{R}{4}$. Accordingly. The resistance of segments DE and EC are $R_{\mathrm{DE}}=R_{\mathrm{EC}}=\frac{R}{8}$.

We can draw the resultant circuit as follows:

Hence,

$\frac{1}{{\mathrm{R}}_{\mathrm{e}\mathrm{q}}}=\frac{8}{\mathrm{R}}+\frac{8}{7\mathrm{R}}$
$\frac{1}{{\mathrm{R}}_{\mathrm{e}\mathrm{q}}}=\frac{56+8}{7\mathrm{R}}$
${\mathrm{R}}_{\mathrm{e}\mathrm{q}}=\frac{7\mathrm{R}}{64}$