The distance from Jacksonville to Tampa is 171 miles. The distance from Tampa to Miami is 206 miles. Use the Triangle Inequality Theorem to find the range for the distance from Jacksonville to Miami.
A.35 mi < d < 377 mi
B.0 mi < d < 377 mi
C.-35 mi < d < 377 mi
D.0 mi < d < 35 mi
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Let's call Jacksonville = J , Tampa = T and Miami = M
So distance from J --> T = 171 miles
and distance from T-->M = 206 miles
now we have the following form:
J --> T = 171 miles
T--> M = 206 miles
now let's subtract both equations:
T--> M = 206 miles
- J -->T = 171 miles
(answer) J-->M = 206 - 171
= 35 miles
When you subtract both forms, the T(s) will cancel and become 0 , so you'll be left with J--M , which is the distance from Jacksonville to Miami = 35 miles
that's the smallest distance, which is the smallest range since we have subtracted, now to find the biggest distance add and you'll get 377 miles :)
Did you understand it? ^_^
Answer = (A) :) Correct me if I'm wrong.
The triangular inequality rule states "The sum of any two sides always exceed the length of the third side.
Answer A seems likely, it seems to pin it down close than choice B