Question 1084198
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We're given
first side = 10 ft
second side = 16 ft


Let x be the third side


The sum of any two sides must be larger than the other side
This is what the <a href="http://www.mathwarehouse.com/geometry/triangles/triangle-inequality-theorem-rule-explained.php">triangle inequality theorem</a> is about.


(first side) + (second side) > third side
10 + 16 > x
26 > x
x < 26


(first side) + (third side) > second side
10 + x > 16
10 + x - 10 > 16 - 10
x > 6


(second side) + (third side) > first side
16 + x > 10
16 + x-16 > 10-16
x > -6


So we know
x > -6
x > 6
x < 26


The two inequalities x > -6 and x > 6 can be absorbed together to get x > 6. So we really have two inequalities which are
x > 6
x < 26


Combine them to form one compound inequality
x > 6 and x < 26
6 < x and x < 26
6 < x < 26


Therefore, the third side x is between 6 and 26. 
The third side cannot be equal to 6.
The third side cannot be equal to 26.


As a shortcut you can use the following
a-b < c < a+b
where
a,b are the two known sides of the triangle (a > b)
c is the unknown side
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