Question

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,

Answer 1

100<x<500

Explanation:

We can create a system of inequalities by using the Triangle Inequality Theorem. This theorem states that the sum of two sides on a triangle is greater than the other sides.
1.) Figure out the first inequality. This would be 300+200>x, or x<500.

2.) Figure out the second inequality. This would be x + 200 > 300, or x>100.
3.) Figure out the third inequality. This would be x + 300 > 200, or x > -100.

4.) Combine these inequalities. By combining these inequalities, we would get 100<x<500.