1)) A triangle has two sides of length 17.4 and 14.7 What compound inequality describes the possible lengths for the third side x? 1) Write a compound inequality like 1lt xlt 3 square

Question

1)) A triangle has two sides of length 17.4 and 14.7 What compound inequality describes the possible lengths for the third side x? 1) Write a compound inequality like 1lt xlt 3 square

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: Applying the Theorem### Let

and

. Let

be the length of the third side,

. We have:

,

, and

.## Step 3: Simplifying the Inequalities###

simplifies to

or

simplifies to

. Since lengths are positive, this becomes

.

simplifies to

.## Step 4: Combining the Inequalities### Combining

, we get

.

Question

1)) A triangle has two sides of length 17.4 and 14.7 What compound inequality describes the possible lengths for the third side x? 1) Write a compound inequality like 1lt xlt 3 square

Solution

Answer

Explanation