Another question. is very much appreciated! ! (see attachment)

The triangle inequality says the two smallest sides have to add up to strictly more than the biggest. So when 7 and 12 are the smaller sides the biggest can't be 19 or larger. When 12 is the largest side the smallest side can't be 5 or smaller. So we check those in the open interval (5,19):

A B C D

According to the triangle inequality theory the sum of 2 sides of a triangle need to be grater than the 3rd side.

If we sum 7 + 12 we obtain a result of 19. Since nineteen is the answer, we select all the options that summed with either 12 or 7 are lower than 19 but greater than 5 (because if you sum up 5 with the numbers, the answers won't match according to the theory):

A, B, C & D

Hope it helped,

Happy homework/ study/ exam!

step-by-step explanation: