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Could , and be the side lengths of a triangle?Choose answer:(A) Yes(B) No
Full solution
Q. Could , and be the side lengths of a triangle?Choose answer:(A) Yes(B) No
- Check Triangle Inequality Theorem: To determine if three lengths can form a triangle, we 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. We will check this for all three combinations of sides.
- Calculate First Combination: First, we check if . Performing the calculation, we get .
- First Combination Result: The sum of and is not greater than , so the lengths , , and cannot form a triangle according to the triangle inequality theorem.
- Conclusion: Since one of the conditions of the triangle inequality theorem is not satisfied, we do not need to check the other conditions. We can conclude that these lengths cannot form a triangle.
