Question

can a triangle have sides with the given lengths? explain.
1 ft, 4 ft, 9 ft

choose the correct statement below.
○ a. no, because 9 + 1 > 4 contradicts the triangle inequality theorem.
○ b. yes, because 1 + 4 < 9 satisfies the triangle inequality theorem.
○ c. yes, because 9 + 1 > 4 satisfies the triangle inequality theorem.
○ d. no, because 1 + 4 < 9 contradicts the triangle inequality theorem.

Explanation:

Step1: Recall the triangle inequality theorem

For three side lengths \(a\), \(b\), and \(c\) of a triangle, the following must hold: \(a + b>c\), \(a + c>b\), and \(b + c>a\).

Step2: Check the given side lengths \(a = 1\), \(b = 4\), \(c = 9\)

Check \(a + b\) and \(c\): \(1+4=5\), and \(5<9\). This violates the triangle - inequality theorem.

Answer:

D. No, because \(1 + 4<9\) contradicts the triangle inequality theorem.