Question

assignment #9: triangle inequality theorem
find the range of possible values for x using the triangle inequality theorem.
9.
10.

1. <x<
2. <x<

Explanation:

Step1: Apply Triangle Inequality Theorem

The Triangle Inequality Theorem states that for a triangle with side lengths \(a\), \(b\), and \(c\), \(|a - b| < c < a + b\).

Step2: Solve for problem 9

For the triangle with side lengths \(8\), \(3\), and \(x\):

• Lower - bound: \(|8 - 3|=5\)
• Upper - bound: \(8 + 3 = 11\)

So, \(5 < x < 11\)

Step3: Solve for problem 10

For the triangle with side lengths \(12\), \(5\), and \(x\):

• Lower - bound: \(|12 - 5| = 7\)
• Upper - bound: \(12+5 = 17\)

So, \(7 < x < 17\)

Answer:

1. \( 5 < x < 11 \)
2. \( 7 < x < 17 \)