Question

Find three objects (sticks, utensils, yarn, toys, books, etc.) that could represent
the sides of a triangle. Can you make a triangle with these three objects? Use the
Triangle Inequality Theorem explain why or why not

Answer 1

To determine if three objects can form a triangle using the Triangle Inequality Theorem, we first need to choose three objects and measure their lengths. Let's use the following objects:

1. A stick that is 7 inches long.
2. A piece of yarn that is 5 inches long.
3. A ruler that is 3 inches long.

According to the Triangle Inequality Theorem, for three lengths (let's call them **a**, **b**, and **c**) to form a triangle, the following conditions must be satisfied:

1. **a + b > c**
2. **a + c > b**
3. **b + c > a**

Let's assign the lengths:

- **a = 7 inches** (stick)
- **b = 5 inches** (yarn)
- **c = 3 inches** (ruler)

Now, we can test the conditions:

1. **a + b > c**
- 7 + 5 > 3
- 12 > 3 ✔️

2. **a + c > b**
- 7 + 3 > 5
- 10 > 5 ✔️

3. **b + c > a**
- 5 + 3 > 7
- 8 > 7 ✔️

Since all three conditions of the Triangle Inequality Theorem are satisfied, we can conclude that **the three objects can indeed form a triangle**.