SOLUTION: A triangle has two sides that have lengths of 16 inches and 28inches. Which of the following lengths could not represent the lenth of the third side? A.12in. B.26in. c.33in.

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In this particular problem, one must realize this theorem;

In any triangle, the lengths of the two smaller sides must add up to be greater than the length of the long side (not greater than or equal to GREATER)

Example;
Can sides 2 , 10 and 13 make a triangle?
Well the two smaller sides 2 and 10 add up to 12 which is less than the larger side, 13...so the answer is no.

In your problem, check all of the choices, the one that is EQUAL to the larger side or LESS than the larger side is the answer.

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The longest side of a triangle must be LESS than the sum of the other two sides.
There are two possible problems here.

First, if the two smaller sides of the triangle are 16 and 28, then the third side must be LESS than the sum of 16 + 28 or 44. All of the choices given are smaller than 44, and therefore acceptable possibilities.

Second, if the two smaller sides are 16 and the unknown side (call it x), then the third side 28 must be less than the sum of 16 + x. That is,
28 <16 + x
28-16 < 16-16+x
12
This means that x>12, so the unknown side CANNOT be 12 A.

R^2 at SCC