CITIES The distance between New York City, New York, and Boston, Massachusetts, is 187 miles, and the distance between New York City and Hartford, Connecticut, is 97 miles. Hartford, Boston, and New York City form a triangle on a map. What must the distance between Boston and Hartford be greater than?
Question
CITIES The distance between New York City, New York, and Boston, Massachusetts, is 187 miles, and the distance between New York City and Hartford, Connecticut, is 97 miles. Hartford, Boston, and New York City form a triangle on a map. What must the distance between Boston and Hartford be greater than?
Solution
The distance between Boston and Hartford must be greater than the difference between the distance from New York City to Boston and the distance from New York City to Hartford. This is because in a triangle, the length of one side must always be less than the sum of the lengths of the other two sides, but also greater than the absolute difference of the lengths of the other two sides.
The difference between the distance from New York City to Boston (187 miles) and the distance from New York City to Hartford (97 miles) is 187 - 97 = 90 miles.
Therefore, the distance between Boston and Hartford must be greater than 90 miles.
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