Answer: Choice A) 24.0
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Explanation:
Let's say we had a triangle with side lengths a,b,c.
If we know that a = 12.25 and b = 12.25, then the third side c has its length restricted in such a way that
b-a < c < b+a
This is a variation of the triangle inequality theorem.
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So,
b - a < c < b + a
12.25 - 12.25 < c < 12.25 + 12.25
0 < c < 24.5
which means the third side c is between 0 inches and 24.5 inches.
The value of c cannot be 0, and it cannot be 24.5 either.
Among the answer choices given, we see that only 24.0 is the only valid option here. The other two choices are too large.
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Side Note: If your teacher gave you two angles (instead of two sides) to be 12.25 degrees, and wanted the third missing angle of the triangle, then you would be correct in having 12.25+12.25+x = 180 as your first step.
