Question

If a triangle has lengths of 31 and 28, check all the possible lengths for the third side.

Answer 1

To find the possible lengths for the third side of a triangle with lengths 31 and 28, we need to use the triangle inequality theorem. The possible lengths for the third side are between 3 and 59.

Step-by-step explanation:

To determine the possible lengths for the third side of a triangle, we need to consider the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, we have sides of lengths 31 and 28. So, for the third side:

• The sum of 31 and 28 must be greater than the third side length
• The difference between 31 and 28 must be less than the third side length

Therefore, the possible lengths for the third side will satisfy the inequalities: 31 + 28 > third side and 31 - 28 < third side. Solving these inequalities, we get: 3 < third side < 59.