Question

kitchen triangle in exercises 27 and 28, use the following information. the term “kitchen triangle” refers to the imaginary triangle formed by three kitchen appliances: the refrigerator, the sink, and the range. the distances shown are measured in feet. 28. can a kitchen triangle have the following side lengths: 9 feet, 3 feet, and 5 feet? explain why or why not.

Explanation:

Step1: Apply the triangle inequality theorem

The triangle inequality theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\), the following must hold: \(a + b>c\), \(a + c>b\), and \(b + c>a\). Let \(a = 3\), \(b = 5\), and \(c = 9\).

Step2: Check the first inequality

Check \(a + b>c\): \(3+5 = 8\). Since \(8<9\) (i.e., \(3 + 5
ot>9\)).

Answer:

No, a triangle with side lengths 9 feet, 3 feet, and 5 feet cannot exist. Because when applying the triangle - inequality theorem (\(a + b>c\) where \(a = 3\), \(b = 5\), \(c = 9\)), \(3+5=8<9\), which violates the triangle - inequality theorem.