A triangle has side lengths of 14 cm and 5 cm. which could be the value of the third side, 21 cm or 15 cm?

A triangle with sides of 14 and 5 can have as its third side a length that is greater than the difference of the 2 sides (14 - 5 = 9).

So third side must be longer than 9 and shorter than the sum of the 2 sides (14 + 5 = 19). So the third side must be:

9 < third side < 19

So with the choice of a third side being 21 or 15, only thr side of 15 can form a triangle.