The triangle inequality theorem says that the sum of the lengths of any two sides of the triangle must be greater than the length of the third side (see picture) and this must be true for all sides for it to be a real triangle
Let's say a = 17 ft, b = 36 ft, and c = 16ft.
We know that:
[tex]a + b \ \textgreater \ c\\
a + c \ \textgreater \ b\\
b + c \ \textgreater \ a[/tex]
Plug our numbers in and check whether each inequality is true or not. If they are all true, then the dimensions are possible. If one or more isn't true, then the dimensions are not possible:
[tex]17 + 36 = 53\ \textgreater \ 16 \:\:\:\: True\\
17 + 16 = 33 \ \textgreater \ 36 \:\:\:\: False\\
36 + 16 = 52 \ \textgreater \ 17 \:\:\:\: True[/tex]
Since a + c (17+16) is not greater than b (36), the dimensions are not possible because it does not follow the triangle inequality theorem.
