SOLUTION: Two sides of a triangle have lengths 7 and 14. Which expression describes the length of the third side? I know the answer is greater than 7 and less than 21, but I cannot figure ou

Algebra ->  Triangles -> SOLUTION: Two sides of a triangle have lengths 7 and 14. Which expression describes the length of the third side? I know the answer is greater than 7 and less than 21, but I cannot figure ou      Log On


   

Question 940670: Two sides of a triangle have lengths 7 and 14. Which expression describes the length of the third side? I know the answer is greater than 7 and less than 21, but I cannot figure out how to get that answer. Please help as soon as possible.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the third side. Then

x+7 > 14
7+14 > x
14+x > 7 (this is obviously true so ignore it)

The first two inequalities are equivalent to x > 7 and x < 21.

In general, if a and b are two sides of a triangle, with a <= b, then the third side c is in the range (b-a, b+a).