Four houses are located at the corners of a square, one mile on a side. You must connect these houses using a network of wires. You can connect them to each other directly, or to switching stations inside the square. The problem is, you only have 2.75 miles of wire. How can you connect all four houses?
If you connect house A to house B to house C to house D, ¾ of the perimeter, all the houses are connected, but that consumes 3 miles of wire. You will need one or more connecting points inside the square

Question

Four houses are located at the corners of a square, one mile on a side.  You must connect these houses using a network of wires.  You can connect them to each other directly, or to switching stations inside the square.  The problem is, you only have 2.75 miles of wire.  How can you connect all four houses?
If you connect house A to house B to house C to house D, ¾ of the perimeter, all the houses are connected, but that consumes 3 miles of wire.  You will need one or more connecting points inside the square

dumbcow · Answer

well if you have a switching station in the center with wires going out to all 4 houses it will take $$2\sqrt{2}$$ miles
which is close...2.83

anonymous · Answer

$$\large{close}$$

dumbcow · Answer

ok got it
Use 2 switching stations in center separated by horizontal distance (1-2x)
where x is how far they are from outer side of square.
Find a function for total wire length  in terms of x and  minimize.
$$x = \frac{1}{2\sqrt{3}}$$ 
wire length$$L = 2.73$$

dumbcow · Answer

thats a good optimization problem because it also adds logic and reasoning

anonymous · Answer

yaa