Two sides of a triangle are 22 and 34.The length of the third side must be greater than ____ and less than ____.

let the third side be x , where x is a positive number

FACT: the sum of any two sides of a triangle must be greater than the third side, so

22+34 > x AND 22+x > 34 AND 34+x > 22

clearly 34+x is always > 22, so for the other two ...

56 > x AND x > 12

or

12 < x < 56

or, you can use a compound inequality.

34-22 < x < 34+22
12 < x < 56

3B

24

The lengths of two sides of a triangle are 22 inches and 17 inches. Find the range of possible lengths for the third side.

To find the possible range of lengths for the third side of the triangle, you can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's apply this theorem to the given information. The two sides of the triangle are 22 and 34.

To find the minimum length of the third side, we need to determine the smallest sum of the two given sides. Adding the two smallest numbers, which are 22 and 34, we get 56. Therefore, the third side must be greater than 56.

To find the maximum length of the third side, we need to determine the largest sum of the two given sides. Adding the two largest numbers, which are 22 and 34, we again get 56. Therefore, the third side must be less than 56.

In conclusion, the length of the third side must be greater than 56 and less than 56.