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Could , and be the side lengths of a triangle?Choose answer:(A) Yes(B)
Full solution
Q. Could , and be the side lengths of a triangle?Choose answer:(A) Yes(B)
- 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.
- Check st Combination: First, we check if . Performing the calculation, we get , which is true.
- Check nd Combination: Next, we check if . Performing the calculation, we get , which is also true.
- Check rd Combination: Lastly, we check if . Performing the calculation, we get , which is not true.
- Final Conclusion: Since the sum of the lengths of the two smaller sides ( and ) is not greater than the length of the longest side (), the lengths , , and cannot form a triangle according to the triangle inequality theorem.
