Question

In how many ways can we choose one number from the set $\{1,2,3\}$, one number from the set $\{4,5,6\}$, and one number from the set $\{7,8,9\}$ such that the three could be the sides of a nondegenerate triangle

Answer 1

Using triangle concepts, it is found that there are 3 ways to choose a number from each set such that the three could be the sides of a nondegenerate triangle.

What is the condition for 3 lengths to represent a triangle?

In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.

In this problem, the possible lengths are:

• 2, 6 and 7.

• 3, 5 and 7.

• 3, 6 and 8.

Hence, there are 3 ways to choose a number from each set such that the three could be the sides of a nondegenerate triangle.

You can learn more about triangle concepts at https://brainly.com/question/25645873