A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into \(a\) square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is:

For the wire bent into an equilateral triangle, each side has a resistance \(\frac{R}{3}\).

\(R_{\text {eq }}=\frac{\left(\frac{2 R}{3}\right)\left(\frac{R}{3}\right)}{\frac{2 R}{3}+\frac{R}{3}}=\frac{2 R}{9}=R_1\) (lets say)
For the wire bent into a square, each side has a resistance \(\frac{R}{4}\).

\(\begin{aligned} & R_{\text {eq }}=\frac{\left(\frac{3 R}{4}\right)\left(\frac{R}{4}\right)}{\frac{3 R}{4}+\frac{R}{4}}=\frac{3 R}{16}=R_3 \text { (lets say) } \\ & \Rightarrow \frac{R_1}{R_3}=\frac{\frac{2 R}{9}}{\frac{3 R}{16}}=\frac{32}{27}\end{aligned}\)