A: Fill out the Problem-solving boxes to talk yourself through the problem. In the “DO” boxes below, fill in the
blank boxes, picking one number from the integers 1 through 10, at most one time each (cannot reuse any
numbers when picking a new side length) to complete the two scenarios below:
1. A triangle with the side lengths of these numbers that CAN NOT exist. (3pts)
9,11 ,?
Understand & Think (1pt): What is being asked in the problem and what does that mean? What do I know and what does it
mean? What plan am I going to try?
Explanation of my answer and why it makes sense:
The problem is asking if there is a triangle with side lengths of 9, 11, and an unknown number. To determine if this triangle can exist, I need to apply the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.
To answer this question, I will start by checking if 9 + 11 is greater than the third side. 9 + 11 equals 20. Now I will compare this sum to the unknown side length. If the unknown side length is less than or equal to 20, then a triangle can exist. However, if the unknown side length is greater than 20, a triangle cannot exist.
In this case, I need to pick an unknown number that is greater than 20. So my answer is:
9, 11 , 21
This answer makes sense because the sum of 9 + 11 is equal to 20, and any triangle with two sides of lengths 9 and 11 would require the third side to be longer than 20. Therefore, a triangle with side lengths of 9, 11, and 21 cannot exist.