Question

A triangle has two sides of length 10 and 3. What is the smallest possible whole-number length for the third side?

Answer 1

The smallest possible whole-number length for the third side is 8.

Step-by-step explanation:

To find the smallest possible whole-number length for the third side of a triangle with sides of length 10 and 3, we can use the triangle inequality theorem.

According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Therefore, we have two scenarios to consider:

1. The sum of the lengths of the two known sides (10 and 3) is less than the length of the unknown side. In this case, the length of the unknown side must be greater than 10 - 3 = 7.
2. The sum of the lengths of the two known sides is equal to or greater than the length of the unknown side. In this case, the length of the unknown side must be greater than 10 + 3 = 13.

Since we are looking for the smallest possible whole-number length, the smallest whole-number length for the third side is 8.