Final answer:
The equivalent resistance between one end and the midpoint of the side of a wire bent in the form of a triangle is the same as the resistance of one side of the triangle.
Step-by-step explanation:
To find the equivalent resistance of a system where a wire is bent in the form of a triangle and we are looking for the resistance between one end and the midpoint of the side, we use parallel and series resistance equations.
If the original resistances of the wire's sides are R, then the side across from the point of interest is R since it's not altered, but the sides connected to that point each form a section that is half the length of the wire, and have half the resistance (R/2), assuming uniform wire and resistance.
Therefore, those two sections are in parallel, and their combined resistance is (1/(1/(R/2) + 1/(R/2))) = R/2. This parallel resistance is then in series with the opposite full-length side so the total equivalent resistance is R/2 + R/2 = R.