Answer: C) 42 inches
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Step-by-step explanation:
Let's say we have a triangle with sides x,y,z
Also, let's further say we know that x = 19 and y = 28 (from AB and BC respectively).
The third missing side z can't be nailed down to a single number, but we can establish a possible range. That range is
y-x < z < y+x
28-19 < z < 28+19
9 < z < 47
So any number between 9 and 47, excluding both endpoints, will work as a possible side length for the third missing side.
Something like 7 inches is too small, so we rule out choice B. Choice D is ruled out since 49 inches is too big. Same goes for choice A also.
The only thing left is choice C. The 42 is between 9 and 47
In other words, 9 < 42 < 47 is true.
So that's why the third missing side could be 42 inches.
Side note: I'm using a modification of the triangle inequality theorem.