Question

Find the range for the measurement of the third side of a triangle, x, given the measures of the two sides: 6 ft and 13 ft.

Answer 1

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Answer 2

Let side a = 6. Let side b = 13. 3rd side = c is to be found.
The theorem says :"Any side of a triangle must be less than the other two sides added together"
so
a < b+c, b < a+c, and c < a+b

Substituting:
6 < 13+c, 13 < 6+c, and c < 6+13

Solving all three for c:
-7 < c, 7 < c, c < 19

The first one is true, length of side cannot be negative, it must be positive,so ignore it.
Put the second and third together and get
7 < c < 19

That's it. c must be more than 7 and less than 19.