The distance between Lincoln, NE, and Boulder, CO, is about 500 miles. The distance between Boulder, CO, and a third city is 200 miles. Assuming the three cities make a triangle on the map, which values represent the possible distance, d, in miles, between Lincoln, NE, and the third city?
2 answers:
We know that
The sum of the lengths of any two sides of a triangle is greater than the length of the third side (Triangle Inequality Theorem)
Let
A------> Lincoln, NE
B------> Boulder, CO
C------> third city
we know that
in the triangle ABC
AB=500 miles
BC=200 miles
AC=x
Applying the Triangle Inequality Theorem
1) 500+200 > x------> 700 > x------> x < 700 miles
2) 200+x > 500----> x > 500-200------> x > 300 miles
the solution for x is
300 < x < 700
the interval is------> (300,700)
the possible distances, d, in miles, between Lincoln, NE, and the third city, are in the range between 300 and 700 miles
Answer:
300 and 700 I just did it I hoped it helped
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