Question

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?

Answer 1

300<d<700

Explanation:

Answer 2

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