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 ,?(1,2,3,4,5,6,7,8,9,10)
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?
Do/Answer (2pts): I will write out my response to the question,
explaining my answer and what it means. I will explain why my
answer makes sense. (Fill in the missing length in the empty box.)
Explanation of my answer and why it makes sense:
Understand & Think: The problem is asking for a triangle with the given side lengths that cannot exist. This means that the side lengths are not valid for creating a triangle. I know that in order for a triangle to exist, the sum of the lengths of any two sides must be greater than the length of the third side. I will try to find a combination of side lengths that does not satisfy this condition.
Do/Answer: The combination of side lengths that does not satisfy the condition is 9, 11, and 10. According to the triangle inequality theorem, the sum of the lengths of any two sides must be greater than the length of the third side. However, in this case, 9 + 11 is equal to 20, which is not greater than 10. Therefore, a triangle with side lengths 9, 11, and 10 cannot exist.
Explanation of my answer and why it makes sense: This answer makes sense because it follows the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this scenario, the sum of 9 and 11 is not greater than 10, so a triangle cannot be formed using these side lengths.