16.Which Three Lengths CANNOT be the lengths of the sides of a triangle? 17.Which Three Lengths COULD-BE the lengths of the sides of a triangle?

Problem 16

This is because the two smaller sides 8 and 10 add to 8+10 = 18, but this is not greater than the side 21. For a triangle to be possible, the sum of any two sides must be larger than the third side. I recommend cutting out slips of paper of these lengths to confirm that a triangle is indeed not possible in this case.

Problem 17

Choice A is not the answer because 13+8 = 21, but that's not larger than the third side 21.

Choice C is not the answer because 6+11 = 17 which is not larger than 24.

Choice B is the only possible answer. Note we have the three following true inequalities

So adding any two sides of this triangle leads to a sum larger than the third side. We're using the triangle inequality theorem.