Question

Which of the following sets of numbers can be the lengths of the sides of a

triangle?
(A) 12,9, 4
(B) 1, 2, 3
(C) 5, 5, 10
(D) √2, √5,√18

Answer 1

A triangle can be formed if the sum of the lengths of any two sides is greater than the length of the third side. Only set (C) 5, 5, 10 meets this criteria.

Step-by-step explanation:

A triangle can be formed if the sum of the lengths of any two sides is greater than the length of the third side. Let's check each set of numbers:

1. (A) 12, 9, 4: In this case, 12 + 9 is not greater than 4, so it cannot be a triangle.
2. (B) 1, 2, 3: Here, 1 + 2 is equal to 3, so it cannot be a triangle.
3. (C) 5, 5, 10: The sum of any two sides is always greater than the third side in this set, so it can form a triangle.
4. (D) √2, √5, √18: We can't determine if this forms a triangle without knowing the exact values of the square roots.

Therefore, the set of numbers that can be the lengths of the sides of a triangle is (C) 5, 5, 10.

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