Question

Judy says that she built a triangular garden over the weekend and that the sides measure 17 feet, 36 feet, and 16 feet. Are these dimensions possible? Yes or No? and why?

Answer 1

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:
$a + b \ \textgreater \ c\\ a + c \ \textgreater \ b\\ b + c \ \textgreater \ a$
 
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:
$17 + 36 = 53\ \textgreater \ 16 \:\:\:\: True\\ 17 + 16 = 33 \ \textgreater \ 36 \:\:\:\: False\\ 36 + 16 = 52 \ \textgreater \ 17 \:\:\:\: True$

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.