The Triangle Inequality Theorem is fundamental in determining whether three lengths can form a triangle. It states that for any three sides of a triangle, the sum of the lengths of any two sides must always be greater than the length of the third side. This theorem is widely applicable in various fields, including engineering, architecture, and computer graphics, where spatial relationships must be assessed. For example, in structural design, ensuring that supports can form triangles guarantees stability and strength. Additionally, the theorem helps in optimizing routing problems in network design, ensuring efficient connections between points.
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:
Book + Pencil > Straw
→ (True)
Book + Straw > Pencil
→ (True)
Pencil + Straw > Book
→ (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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