1. Is it possible to form a triangle with side lengths 6,9 , and \( 16 ? \) 2.

To determine if these side lengths can form a triangle, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side. Here, let's check: 1. \(6 + 9 > 16\) is \(15 > 16\) (false). 2. \(6 + 16 > 9\) is \(22 > 9\) (true). 3. \(9 + 16 > 6\) is \(25 > 6\) (true). Since one condition fails, side lengths of 6, 9, and 16 cannot form a triangle. Now, let's have a little fun with this! Imagine all three sides are at a party, trying to mingle and giggle, but when it comes to forming a tight-knit triangle, 6 and 9 realize they just can't keep up with the much longer and lonelier 16! If you're ever unsure, just remember that triangle inequality is your friend. When you're working with potential triangle lengths, always test them out! Gather your lengths and check if each pair can join with the third side—if one can't, it's like being left out of a club: no triangle for you!