Question

Determine whether the given measures can be the lengths of the sides of a triangle. Write yes or no and write an inequality to verify the relationship.

3, 5, 9
a) Can the given measures be the lengths of the sides of a triangle?
Yes
No
1, 3, 5
a) Can the given measures be the lengths of the sides of a triangle?
Yes
No

Answer 1

For the measures 3, 5, 9, the lengths can be the sides of a triangle. However, for the measures 1, 3, 5, they cannot form a triangle.

Step-by-step explanation:

To determine whether the given measures can be the lengths of the sides of a triangle, we need to check if the sum of the lengths of any two sides is greater than the length of the third side. Let's analyze each case:

1. For the measures 3, 5, 9, we check if 3 + 5 > 9, 3 + 9 > 5, and 5 + 9 > 3. Since all these inequalities hold true, the measures can be the lengths of the sides of a triangle.
2. For the measures 1, 3, 5, we check if 1 + 3 > 5, 1 + 5 > 3, and 3 + 5 > 1. However, the inequality 1 + 5 > 3 does not hold true. Therefore, the measures cannot be the lengths of the sides of a triangle.