If a triangle has two sides of length 5, what is the minimum length of the third side?

• A. 0
• B. 1
• C. 5
• D. 10

Answer: (B)

To determine the minimum length of the third side of a triangle with two sides measuring 5 units each, we can apply 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 remaining side.

In this scenario, we have two sides of length 5. Let's denote the third side as ( x ). According to the triangle inequality, we can derive the following inequalities:

1. ( 5 + 5 > x ) (which simplifies to ( 10 > x ))

2. ( 5 + x > 5 ) (which simplifies to ( x > 0 ))

3. ( 5 + x > 5 ) (which is the same condition as the previous one)

The second inequality tells us that ( x ) must be greater than 0. This indicates that the smallest possible length for the third side, while still allowing the shape to remain a triangle, is just over 0. Hence, the minimum feasible length for the third side, rounded to the nearest whole number in this context, is 1.

Thus, having 1 as the answer reflects the necessary condition that the length must be positive