Triangle inequality
In each triangle, any two sides together are longer than the remaining third side. So, the following applies for their lengths in each type of triangle:
$$a+b>c$$
$$c+b>a$$
$$a+c>b$$
E.g. if we have the given lengths of two sides of the triangle a = 8, b = 3, c = 6, we can construct the triangle. But if the sides are a = 3, b = 4, c = 9, the triangle cannot be constructed because:
$$3 + 4 <9$$
If we know only two lengths (e.g. a = 3 and b = 7) and we have to find out the possible range of the length of the side c, we proceed as follows:
$$a + b> c ;→;3+7>c$$
$$;→; c <10$$
At the same time
$$ a+c > b ;→; 3+c > 7$$
$$ ;→; c > 4$$
And also:
$$b+c>a ;→;7+c>3$$
$$ ;→; c>0$$
So we know:
$$c<10$$
$$c>4$$
$$c>0$$
In order for c to satisfy all of these inequalities, its length must be between 4 and 10:
$$4
