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
Hey ya'll! I'm posting another question like the one I just posted. Do you think you guys can help me out with this or tell me how I can do it? I'm not that good at geometry. Thank you so much if you do!
okay, so judging by the explanation, I need to find the sum of the math you gave me, and if the first two are greater then the third expression, then it can form a triangle? am I understanding right?
I looked the expressions up and this is the results
1. true
2. true
3. false
does this mean I can form a triangle?
The sum of any two sides must be greater than the third side to physically form
the triangle, so is ...
20.2 + 11 > 8.2 ?
is 20.2 + 8.2 > 11 ?
is 11 + 8.2 > 20.2 ?
if the answer to any of those is NO, then you can't have a triangle
ohhh, sorry, i misunderstood!
Of course! I can help you determine if the given side lengths can form a unique triangle, many different triangles, or no triangles. In order to do that, we can use the Triangle Inequality Theorem.
The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
So, let's check if the given side lengths follow this theorem:
First, let's take the sum of the two smaller sides and compare it with the length of the longest side. We have:
11 in + 8.2 in = 19.2 in.
Since 19.2 in is less than 20.2 in, the sum of the two smaller sides is not greater than the length of the longest side.
Therefore, according to the Triangle Inequality Theorem, it is not possible to form a triangle with these side lengths.
So, the answer to your question is:
C. no triangles.
did you not read my last line ?
"if the answer to any of those is NO, then you can't have a triangle"