QuestionWhat is the minimum distance between Boston and Hartford if NYC, Boston, and Hartford form a triangle?
Studdy Solution
STEP 1
Assumptions1. The distance between New York City and Boston is187 miles. The distance between New York City and Hartford is97 miles3. The distances form a triangle, with each city representing a vertex of the triangle
STEP 2
In a triangle, the length of one side must be less than the sum of the lengths of the other two sides. This is known as the triangle inequality theorem.So, the distance between Boston and Hartford must be less than the sum of the distances between New York City and Boston, and New York City and Hartford.
STEP 3
Now, plug in the given values for the distances between New York City and Boston, and New York City and Hartford.
STEP 4
Calculate the sum of the distances.
So, the distance between Boston and Hartford must be less than284 miles.
STEP 5
However, the problem asks for the distance that the distance between Boston and Hartford must be greater than. This is the absolute difference between the distances from New York City to Boston and New York City to Hartford.
STEP 6
Now, plug in the given values for the distances between New York City and Boston, and New York City and Hartford.
STEP 7
Calculate the absolute difference of the distances.
So, the distance between Boston and Hartford must be greater than90 miles.
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