Make a triangle, thats easy to measure, and find three common objects in a house, like three sticks etc. Tell me what to use to make the triangle. Can you make a triangle with these objects? Use the Triangle Inequality Theorem explain why or why not.

Answer 1

Sure! Let's create a triangle using three common household objects. Here are three objects you can use:

1. Books (or thick magazines)
2. Pencils (or pens)
3. Straws

Steps to Make the Triangle:

1. Choose the Lengths:

   • Select three objects and measure their lengths. Here are some example lengths you might use for each object:
     • Book 1: 12 inches
     • Pencil: 8 inches
     • Straw: 5 inches

2. Arrange the Objects:

   • You will place the three objects such that each object represents one side of the triangle, with their ends touching to form the vertices.

Using the Triangle Inequality Theorem:

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. So, for our example lengths, we need to check if the following conditions hold true:

1. Book + Pencil > Straw

   • \( 12 + 8 > 5 \) → \( 20 > 5 \) (True)

2. Book + Straw > Pencil

   • \( 12 + 5 > 8 \) → \( 17 > 8 \) (True)

3. Pencil + Straw > Book

   • \( 8 + 5 > 12 \) → \( 13 > 12 \) (True)

Conclusion:

Since all three conditions of the Triangle Inequality Theorem are satisfied, you can indeed make a triangle with the chosen lengths of the books, pencils, and straws. If you follow these steps, you should be able to form a triangle using those common household objects!