Let a, b, and c be the length of 3 corresponding sides of the triangle. The following inequality must always be true since they form a triangle :
[tex]a+b>c[/tex]
(This inequality says that the sum of two sides must always be greater than the other side)
Let's use this inequality for x, 1.3, and 4.1
[tex]x+1.3>4.1[/tex]
(The reason why 1.3 is on the left side is because it is the smaller side)
Subtract both sides by 1.3
[tex]x>2.8[/tex]
x must always be greater than 2.8. Now, let's see what value x must be always less than.
[tex]1.3+4.1>x[/tex]
[tex]5.4>x[/tex]
x must be always less than 5.4. Let's combine both statements for x and we get:
[tex]2.8<x<5.4[/tex]
These are the only values of x that will make it possible for these sides to form a proper triangle.
Let me know if you need any clarifications, thanks!
~ Padoru
