Answer: Obtuse triangle
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Explanation:
In this case, a triangle is possible since adding any two sides leads to a sum larger than the third side
- 20+23 = 43 is larger than 41
- 20+41 = 61 is larger than 23
- 23+41 = 64 is larger than 20
I'm using the triangle inequality theorem here.
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To determine what kind of triangle we have, we'll use the converse of the Pythagorean theorem. Specifically, we'll use a corollary of it.
Consider a triangle with sides a,b,c. Let c be the longest side.
We have three possible cases:
- If a^2+b^2 = c^2, then we have a right triangle
- If a^2+b^2 > c^2, then the triangle is acute.
- If a^2+b^2 < c^2, then the triangle is obtuse.
For this problem, we have a = 20, b = 23, c = 41.
We see that a^2+b^2 = 20^2+23^2 = 929 and c^2 = 41^2 = 1681.
In short, a^2+b^2 = 929 and c^2 = 1681.
Since 929 < 1681, this means a^2+b^2 < c^2.
Therefore, this triangle is obtuse.
