<p>If the length of line AB is 5 and the length of line BC is 6, which of the following could be the length of line AC?
A) 10
B) 12
C) 13
D) 15
E) 16</p>
<p>I chose B thinking it couldn't be 10 (as 5+6 is greater than that), but can't be more than one off or something.
The unique part of my thread is that there's a stain right where it told me the answer for this one, so I can't tell you what the real answer actually is.
Any ideas?</p>
<p>The answer is A.</p>
<p>Your reasoning is a little off. 5+6 is greater than 10, so 10 is the only correct answer. Remember that in a triangle, one side must be LESS than the sum of the other two sides, not greater. Looks like just a silly mistake.</p>
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</p>
<p>Thanks, didn’t think of it that way.
I was unsure whether or not they referred to a triangle or just 2 combined line segments; I even tried using Pythagorean theorem to see if there was a match, but didn’t think about the any 2 sides must be greater than the third property.</p>
<p>This is a triangle rule question. The third side of a triangle is between the difference and sum of the other 2 sides. In this case the difference is 6-5=1, and the sum is 6+5=11. Choice (A) is the only answer between these 2 numbers.</p>
<p>Remark: In this problem it is possible for the answer to be 1 or 11 (these are the extreme cases where you get lines instead of triangles), but it is irrelevant since neither of these are answer choices.</p>
<p>@DrSteve</p>
<p>Thanks for that explanation of yours. I didnt know it.</p>
<p>You gotta watch out for the “could be” part in questions.</p>