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Determine if the segment lengths form a triangle. If so, would the triangle be acute, right, or obtuse? 4.1, 8.2, 12.2

ANo, they do not form a triangle.
BYes, they would form an acute triangle.
CYes, they would form a right triangle.
DYes, they would form an obtuse triangle

Verified Answer :

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Three line segments can form a triangle if the length of the longest segment is greater than the sum of the lengths of the shorter segments.

 \(4.1 + 8.2 \ \textgreater \ 12.2 \\ 12.3 \ \textgreater \ 12.2 \\ true\)
They can form a triangle.

Now if c is the length of the longest side and a and b are the lengths of the shorter sides, then:
- if \(c^2=a^2+b^2\), the triangle is right
- if \(c^2\ \textless \ a^2+b^2\), the triangle is acute
- if \(c^2\ \textgreater \ a^2+b^2\), the triangle is obtuse

\(4.1^2+8.2^2=16.81+67.24=84.05 \\ 12.2^2=148.84 \\ \\ 148.84\ \textgreater \ 84.05\)
The triangle is obtuse.

The answer is D.

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