Question

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

Answer 1

To determine whether three objects can form a triangle, we can use the Triangle Inequality Theorem. This theorem states that for any three sides of a triangle (let's call them a, b, and c), the following conditions must be satisfied:

1. \( a + b > c \)
2. \( a + c > b \)
3. \( b + c > a \)

Let's say we choose the following three objects, each with a length representing one side of a triangle:

1. A stick that is 5 units long.
2. A rope that is 7 units long.
3. A pencil that is 3 units long.

Now, we can represent these lengths with the variables:
- \( a = 5 \)
- \( b = 7 \)
- \( c = 3 \)

Next, we can apply the Triangle Inequality Theorem:

1. Check \( a + b > c \):
\[
5 + 7 > 3 \quad \text{(12 > 3 is true)}
\]

2. Check \( a + c > b \):
\[
5 + 3 > 7 \quad \text{(8 > 7 is true)}
\]

3. Check \( b + c > a \):
\[
7 + 3 > 5 \quad \text{(10 > 5 is true)}
\]

Since all three conditions are satisfied, the three objects (the stick, rope, and pencil) can indeed form a triangle.

Thus, based on the Triangle Inequality Theorem, we can conclude that it is possible to create a triangle with these three objects.