Find three objects (sticks, utensils, yarn, toys, books, etc.) that could represent

Question

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 represent the sides of a triangle, let's choose three objects of different lengths:

1. A stick that is 5 units long
2. A stick that is 3 units long
3. A stick that is 4 units long

Now we can check if these three objects can form a triangle using the Triangle Inequality Theorem. The theorem states that for any three lengths \( a \), \( b \), and \( c \) to be the sides of a triangle, the following three conditions must be true:

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

Let's assign the lengths as follows:

• Let \( a = 5 \) (the longest stick)
• Let \( b = 3 \)
• Let \( c = 4 \)

Now we'll check the conditions:

1. \( a + b > c \) : \( 5 + 3 > 4 \) → \( 8 > 4 \) (True)
2. \( a + c > b \) : \( 5 + 4 > 3 \) → \( 9 > 3 \) (True)
3. \( b + c > a \) : \( 3 + 4 > 5 \) → \( 7 > 5 \) (True)

Since all three conditions are satisfied, we can conclude that the lengths 5, 3, and 4 can indeed form a triangle.

So, yes, we can make a triangle with these three objects.