A triangle has two sides of length 9 and 12.What is the largest possible whole number length for the third side

The correct answer is - 20.

Explanation:

According to the triangle inequality theorem states that the largest and smallest value of the third side of the triangle can be found with the other two sides. The lowest value would be more than the difference of the other two sides and the largest value would be less than the sum of the other two sides of the triangle.

In this case, the other two sides are - 9 and 12

suppose the third side is - x

Then according to the triangle inequality theorem, the largest value of x would be:

x< 12+9

x< 21

so the x would be less than the 21 which is - 20.