4)) A triangle has two sides of length 6.7 and 15.2. What compound inequality describes the possible lengths for the third side, x? 4) Write a compound inequality like 1lt xlt 3

Question

4)) A triangle has two sides of length 6.7 and 15.2. What compound inequality describes the possible lengths for the third side, x? 4) Write a compound inequality like 1lt xlt 3

Answer 1

## Step 1: Triangle Inequality Theorem### The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This gives us three inequalities:

,

, and

.## Step 2: Solving the Inequalities###

simplifies to

or

simplifies to

or

.

simplifies to

or

. Since side lengths must be positive,

is redundant.## Step 3: Combining the Inequalities### Combining

, we get the compound inequality

.

Question

4)) A triangle has two sides of length 6.7 and 15.2. What compound inequality describes the possible lengths for the third side, x? 4) Write a compound inequality like 1lt xlt 3

Solution

Answer

Explanation