Answer: The length of the third side is greater than 4 ft and less than 20 ft.
Step-by-step explanation: Given that two sides of a triangle have lengths 8 ft and 12 ft.
We are to describe the possible lengths of the third side.
Let x ft be the length of the third side of the triangle.
We know that
the sum of the lengths of any two sides of a triangle is always greater than the third side.
So, we must have
[tex]8+12>x\\\\\Rightarrow 20>x\\\\\Rightarrow x<20~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Also,
[tex]12+x>8\\\\\Rightarrow x>8-12\\\\\Rightarrow x>-4~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
and
[tex]8+x>12\\\\\Rightarrow x>12-8\\\\\Rightarrow x>4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
From inequalities (i), (ii) and (iii), we get
[tex]4<x<20.[/tex]
Thus, the length of the third side is greater than 4 ft and less than 20 ft.
