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(please remove the space in the link above, because I could not post the full problem)
I think that I should use the following: a<b+c ,b<a+c ,c<a+b or the inequality of the means, but I have no idea how to do it.
To solve this problem, you can use the triangle inequality theorem, which states that for any triangle with side lengths a, b, and c:
a < b + c
b < a + c
c < a + b
In this case, you have a diagram representing a triangle with side lengths a, b, and c and a shaded region. To determine the conditions for the shaded region, you can use the triangle inequality theorem.
First, let's label the sides of the triangle in the diagram. Looking at the diagram, it appears that 'a' represents the length of the hypotenuse, 'b' represents the difference between the hypotenuse and the base, and 'c' represents the height.
Now, let's apply the triangle inequality theorem to find the conditions for the shaded region:
1) From the first condition, a < b + c, we know that the length of the hypotenuse (a) must be less than the sum of the difference between the hypotenuse and the base (b) and the height (c).
2) From the second condition, b < a + c, we know that the difference between the hypotenuse and the base (b) must be less than the sum of the length of the hypotenuse (a) and the height (c).
3) From the third condition, c < a + b, we know that the height (c) must be less than the sum of the length of the hypotenuse (a) and the difference between the hypotenuse and the base (b).
These conditions ensure that the lengths of the sides of the triangle satisfy the triangle inequality, which is necessary for the triangle to exist.
To summarize, the conditions for the shaded region in the diagram are:
a < b + c
b < a + c
c < a + b
These conditions ensure that the lengths of the sides of the triangle satisfy the triangle inequality theorem.