the distance between lincoln, ne, and boulder, co, is about 500 miles. the distance between boulder, co, and…

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? <d<

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? <d<

Answer

Explanation:

Step1: Apply triangle inequality theorem

The triangle inequality theorem states that for any triangle with side lengths (a), (b), and (c), (|a - b|\lt c\lt a + b). Let (a = 500) (distance between Lincoln, NE and Boulder, CO) and (b=200) (distance between Boulder, CO and the third city).

Step2: Calculate the lower - bound

The lower - bound is (|500 - 200|). [|500 - 200|=300]

Step3: Calculate the upper - bound

The upper - bound is (500 + 200). [500+200 = 700]

Answer:

(300\lt d\lt700)