Question

enter the correct answer in the box.

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\\).

Explanation:

State the given side lengths

Using the Triangle Inequality Theorem knowledge point
We are given two side lengths of a triangle:

$$ a = 200,\quad b = 300 $$

The third side length is represented by \(x\).

Apply the Triangle Inequality Theorem

Using the Triangle Inequality Theorem knowledge point

$$
LATEXBLOCK0
$$

Combine into a compound inequality

Using the Triangle Inequality Theorem knowledge point

$$ 100 < x < 500 $$

Answer:

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.

<blank>\(100 < x < 500\)</blank>