Final answer:
The range of possible lengths for the third side, x, in a triangle with sides of 200 units and 300 units, according to the Triangle Inequality Theorem, is 100 < x < 500 units.
Step-by-step explanation:
Range of Possible Lengths for the Third Side
To determine the range of possible lengths for the third side of a triangle with two given sides, you can use the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Applied to this problem with sides of 200 units and 300 units, we have two inequalities to create a compound inequality:
- 200 + 300 > x
- 200 + x > 300
- 300 + x > 200
From the first inequality, we get x < 500. The second inequality simplifies to x > 100, and the third inequality is always true since any positive value of x will make the sum larger than 200. Therefore, we can ignore the third inequality in this context.
The compound inequality for the possible length x of the third side is therefore 100 < x < 500 units.