The Triangle Inequality Theorem is a fundamental principle in geometry that asserts the relationship between the lengths of the sides of a triangle. To apply this theorem, one must ensure that the sum of the lengths of any two sides exceeds the length of the third side. For instance, in a scenario where we have lengths representing a book, pencil, and straw, we can evaluate the combinations accordingly. By checking each condition—Book + Pencil > Straw, Book + Straw > Pencil, and Pencil + Straw > Book—we confirm that they each hold true. As all three conditions are satisfied, this demonstrates that it is indeed possible to construct a triangle using these specific lengths.
Write how this apples 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:
Book + Pencil > Straw
12+8>5 arrow pointing right 20 >5
→ (True)
Book + Straw > Pencil
12+5>8 arrow pointing right 17 > 8
→ (True)
Pencil + Straw > Book
8+5>12 pointing right 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!
Write the application of Triangle Inequality theorem in 5 sentences
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