Question

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. The lengths of two sides of a triangle are 15 ft and 29 ft. Find the possible lengths of the third side.

The third side must have a length greater than blank ft and less than blank ft.

Answer 1

The possible lengths of the third side of the triangle are greater than 14 ft and less than 44 ft.

Step-by-step explanation:

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. In this case, the lengths of the two sides are 15 ft and 29 ft.

To find the possible lengths of the third side, we need to consider two scenarios: when the third side is the longest side and when it is the shortest side.

• When the third side is the longest side, its length is less than the sum of the lengths of the other two sides. That means the third side must be greater than 29 - 15 = 14 ft. So, the third side must have a length greater than 14 ft.
• When the third side is the shortest side, its length is greater than the difference between the lengths of the other two sides. That means the third side must be greater than 29 - 15 = 14 ft. So, the third side must have a length greater than 14 ft.

Therefore, the possible lengths of the third side are greater than 14 ft and less than 29 + 15 = 44 ft.