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

Answer 1

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

Answer 2

or, you can use a compound inequality.

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

Answer 3

3B

Answer 4

24

Answer 5

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