Determine if the given side lengths could be used to form a unique triangle, many different triangles, or no triangles.
20.2 in., 11 in., 8.2 in.
A.unique triangle
B.many different triangles
C.no triangles
same question here:
https://www.jiskha.com/questions/1820925/determine-if-the-given-side-lengths-could-be-used-to-form-a-unique-triangle-many
I choose A.
11 + 8.2= 19.2
that is not long enough to reach from 0 to 20.1 even if they are sraight along the long side, fails.
To determine if the given side lengths can form a unique triangle, many different triangles, or no triangles, we need to apply the triangle inequality theorem.
According to the triangle inequality theorem, the sum of the two shorter sides of a triangle must be greater than the length of the longest side.
In this case, let's label the side lengths as follows:
a = 20.2 in.
b = 11 in.
c = 8.2 in.
Now, we need to check the inequalities:
a + b > c
20.2 + 11 > 8.2
31.2 > 8.2
b + c > a
11 + 8.2 > 20.2
19.2 > 20.2
a + c > b
20.2 + 8.2 > 11
28.4 > 11
From these inequalities, we can see that all three conditions are satisfied. Therefore, the given side lengths (20.2 in., 11 in., 8.2 in.) can form a unique triangle.
Therefore, the answer is A. unique triangle.