Answer:
Step-by-step explanation:
8.) For a triangles sides to make sense, you must be able to add up two values of the triangle, and the result should be more than the third side. Add the lowest values and see if the result is greater than the biggest number:
[tex]4.2+7.9=12.1[/tex]
12.1 is less than the given side, 13.3, so a triangle cannot have the lengths.
10.) 6<x<22
To find the range for the third side of the triangle, you need to find how small x can be (the missing side) and you need to see how large it can be.
You need to see how small it can be because any two sides have to be greater than the third side. You also need to see how big it can be because, if it's too big, the other two sides will be less than the third side, which would make an open shape (see picture).
To find the range, first see how small. Subtract the known sides:
[tex]22-6=16[/tex]
So, x has to be greater than 16.
x > 16
Now add the known sides:
[tex]22+6=28[/tex]
x needs to be less than 28 for the other two sides to be greater than x:
x < 28
Insert the inequalities into a single inequality:
16 < x <28
X has to be greater than x, but less than 28.
