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Answer :
Final answer:
Using the triangle inequality theorem, we can determine that the set of lengths that will not form a triangle is 4 cm, 12 cm, 25 cm. This is because the sum of the lengths of the two shorter sides (4 cm and 12 cm) is not greater than the length of the longest side (25 cm).
Explanation:
The subject of the question falls under the realm of Mathematics, more specifically, geometry. The question is asking to identify which set of lengths will not form a valid triangle. To do this, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Looking at the given options:
- 5 inches, 5 inches, 5 inches: This forms an equilateral triangle
- 4 inches, 4 inches, 3 inches: This forms an isosceles triangle
- 16 cm, 17cm, 18cm: This forms a scalene triangle
- 4 cm, 12 cm, 25 cm: This does not form a valid triangle because 4 cm + 12 cm (which equals 16 cm) is not greater than 25 cm.
So, the set of lengths that will not form a triangle is 4 cm, 12 cm, 25 cm.
Learn more about Triangle Inequality Theorem here:
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Rewritten by : Barada
The sets of lengths that will form a triangle are: 5 inches - 5 inches - 5 inches, 4 inches - 4 inches - 3 inches, and 16 cm - 17 cm - 18 cm. The lengths that do not form a triangle are 4 cm, 12 cm, and 25 cm. This conclusion is derived from the Triangle Inequality Theorem.
To determine which set of lengths will NOT form a triangle, we will use the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
- For lengths 5 inches, 5 inches, and 5 inches:
5 + 5 > 5, 5 + 5 > 5, and 5 + 5 > 5. These satisfy the condition and will form a triangle. - For lengths 4 inches, 4 inches, and 3 inches:
4 + 4 > 3, 4 + 3 > 4, and 4 + 3 > 4. These satisfy the condition and will form a triangle. - For lengths 16 cm, 17 cm, and 18 cm:
16 + 17 > 18, 16 + 18 > 17, and 17 + 18 > 16. These satisfy the condition and will form a triangle. - For lengths 4 cm, 12 cm, and 25 cm:
4 + 12 = 16, which is NOT greater than 25. Therefore, they do NOT satisfy the condition and will NOT form a triangle.
Thus, the lengths 4 cm, 12 cm, and 25 cm will NOT make a triangle.
