Question
- ixis Can the sides of a triangle have lengths 17,6 , and 20 ?
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Ask by Lee Fleming. in the United States
Jan 16,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Yes, the sides 17, 6, and 20 can form a triangle.
Solution
Yes, the sides with lengths 17, 6, and 20 can form a triangle.
Explanation:
For three lengths to form a triangle, they must satisfy the triangle inequality theorem, which states that the sum of any two sides must be greater than the third side. Let’s check each combination:
For three lengths to form a triangle, they must satisfy the triangle inequality theorem, which states that the sum of any two sides must be greater than the third side. Let’s check each combination:
-
17 + 6 > 20:
✔️ -
17 + 20 > 6:
✔️ -
6 + 20 > 17:
✔️
Since all three conditions are satisfied, the lengths 17, 6, and 20 can indeed form a valid triangle.
Answer:
Yes
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Simplify this solution The Deep Dive
To determine if three lengths can form a triangle, you can use the triangle inequality theorem. This means that the sum of the lengths of any two sides must be greater than the length of the third side. For your lengths: 17 + 6 = 23 (which is greater than 20), 17 + 20 = 37 (which is greater than 6), and 6 + 20 = 26 (which is greater than 17). Hence, yes, these lengths can indeed form a triangle!
Fun fact! Ancient Greeks were the first to formalize these rules for triangles, laying a foundation for what would become modern geometry. The amazing mathematician Pythagoras often explored the relationships between triangle sides, paving the way for discoveries that effect everything from architecture to physics today!
