Question

Determining Possible Side Lengths

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 1

300 < d < 700

Explanation:

we know thatin the triangle ABCAB=500 milesBC=200 milesAC=xApplying the Triangle Inequality Theorem1) 500+200 > x------> 700 > x------> x < 700 miles2) 200+x > 500----> x > 500-200------> x > 300 milesthe solution for x is 300 < x < 700

Answer 2

300<d<700

Explanation: