235k views
5 votes
A triangle has side lengths of 200 units and 300 units. Write a compound inequality for the range of the possible lengths for the third side, x.

User Geni
by
8.2k points

1 Answer

6 votes

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:

  1. 200 + 300 > x
  2. 200 + x > 300
  3. 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.

User Michal Ostruszka
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories