Question

Given two sides of a triangle, you can set up an inequality using the sum and difference to show the range of possible lengths for the third side 14 and 22 (let x= the third side)

Answer 1

To show the range of possible lengths for the third side of a triangle, we can use the triangle inequality theorem.

Step-by-step explanation:

To show the range of possible lengths for the third side of a triangle, we can use the triangle inequality theorem.

The 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, and the difference between the lengths of any two sides of a triangle must be less than the length of the third side.

In this case, we have two given sides of 14 and 22. Let's set up the inequalities:

• Sum inequality: 14 + 22 > x (where x is the length of the third side)
• Difference inequality: 22 - 14 < x (where x is the length of the third side)

Simplifying the inequalities, we have:

• 36 > x
• 8 < x

Therefore, the range of possible lengths for the third side is x > 8 and x < 36.