Question

Thequalities in Two Triangles Sample work Part 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) 7 11 ? What's my end goal? What connections can I make here? What tools, strategies, etc. can I use?​

Answer 1

The student must apply the triangle inequality theorem to determine a third side length that would prevent the formation of a valid triangle. Choosing a third side length of 12 with given side lengths of 7 and 11 would violate the triangle inequality theorem, resulting in a triangle that cannot exist.

Step-by-step explanation:

The student is dealing with a mathematical problem that involves understanding the properties of triangles. Specifically, they are tasked with choosing a third side length for a triangle with the given side lengths of 7 and 11 that cannot form a valid triangle. The key principle to use here is 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.

To create a triangle that cannot exist, we need a third side such that when added to either 7 or 11, the sum is not greater than the other side. Since 7 + 11 = 18, we need the third side to be a number such that when added to 7 or 11, it does not exceed the remaining side's length. If we pick 12 as the third side, then 7 + 11 is not greater than 12, violating the triangle inequality theorem. Hence, a triangle with side lengths of 7, 11, and 12 cannot exist.