Answer:
A)
C)
E)
F)
Step-by-step explanation:
we know that
The <u>Triangle Inequality Theorem,</u> states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side
Let
a,b,c ------> the length sides of the triangle
in this problem we have
Applying the triangle inequality theorem
1)
-------> -----> inequality A
2)
-------> ------> inequality B
The solution for the length of the third side is the interval----->
------> compound system of inequalities
we're going to verify all the cases
If a value could be the length of the third side, then the value must be satisfy the compound system of inequalities
<u>case A)</u>
Substitute the value in the compound system of inequalities
For
-------> is true
therefore
The value of can be the length of the third side
<u>case B)</u>
Substitute the value in the compound system of inequalities
For
-------> is not true
therefore
The value of cannot be the length of the third side
<u>case C)</u>
Substitute the value in the compound system of inequalities
For
-------> is true
therefore
The value of can be the length of the third side
<u>case D)</u>
Substitute the value in the compound system of inequalities
For
-------> is not true
therefore
The value of cannot be the length of the third side
<u>case E)</u>
Substitute the value in the compound system of inequalities
For
-------> is true
therefore
The value of can be the length of the third side
<u>case F)</u>
Substitute the value in the compound system of inequalities
For
-------> is true
therefore
The value of can be the length of the third side