Question

In triangle ABC, the length of side AB is 12 inches and the length of side BC is 21 inches. Which of the following could be the length of side AC?

27 inches
7 inches
35 inches
38 inches

Answer 1

Triangle Inequality Theorem:

One side of a triangle is less than the sum of the other two.

Answer 2

Take the 21 and 12 that you were given.

Look at the second option: 7 inches

21, 12, 7
--------

Is 21 < 12 + 7 ? Yes or No ---> No, so 7 does not make a triangle with 21 and 12.

Is 12 < 21 + 7 ? Yes or No

Is 7 < 21 + 12 ? Yes or No.

If you get three Yes answers, then 7 could be the third side of the triangle.