Minimum-length roads A house is located at each corner of

Chapter 7, Problem 51E

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QUESTION:

A house is located at each corner of a square with side lengths of 1 mi. What is the length of the shortest road system with straight roads that connects all of the houses by roads (that is, a road system that allows one to drive from any house to any other house)? (Hint: Place two points inside the square at which roads meet.) (Source: Halmos, Problems for Mathematicians Young and Old.)

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QUESTION:

A house is located at each corner of a square with side lengths of 1 mi. What is the length of the shortest road system with straight roads that connects all of the houses by roads (that is, a road system that allows one to drive from any house to any other house)? (Hint: Place two points inside the square at which roads meet.) (Source: Halmos, Problems for Mathematicians Young and Old.)

ANSWER:

Solution Step 1 Consider A BCD as the square and let the houses be located at each corner.

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