Question

Which set of numbers could be the lengths of the sides of a triangle?

A) 2, 5, 4
B) 3, 5, 9
C) 4, 9, 3
D) 17, 15, 2

Answer 1

Option A) with side lengths 2, 5, and 4 is the only set that satisfies the Triangle Inequality Theorem, meaning the sum of any two sides must be greater than the third side for a valid triangle.

Step-by-step explanation:

To determine which set of numbers could be the lengths of the sides of a triangle, we must apply the Triangle Inequality Theorem. This theorem states that for any triangle, the length of any one side must be less than the sum of the other two sides. For example, if you have sides a, b, and c, then a + b > c, a + c > b, and b + c > a must all be true.

Let's apply this test to each option:

• A) 2, 5, 4 - Yes, because 2 + 4 > 5, 2 + 5 > 4, and 4 + 5 > 2.
• B) 3, 5, 9 - No, because 3 + 5 is not greater than 9.
• C) 4, 9, 3 - No, because 4 + 3 is not greater than 9.
• D) 17, 15, 2 - No, because 17 + 2 is not greater than 15.

Only the lengths in option A) satisfy the Triangle Inequality Theorem and could therefore be the lengths of the sides of a triangle.