Question

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question 1 (not answered)
question 1 (multiple choice worth 1 points)
(02.04r lc)
which of the following possibilities will form a triangle?
side = 15 cm, side = 6 cm, side = 8 cm
side = 15 cm, side = 6 cm, side = 9 cm
side = 16 cm, side = 9 cm, side = 6 cm
side = 16 cm, side = 9 cm, side = 8 cm
question 2 (multiple choice worth 1 points)
(02.04r mc)

Explanation:

Step1: Recall triangle inequality theorem

For three side lengths \(a\), \(b\), \(c\) (\(a\leq b\leq c\)), the triangle inequality theorem states that \(a + b>c\).

Step2: Check the first option (\(a = 6\), \(b = 8\), \(c = 15\))

\(6+8=14\), and \(14<15\). So, these side - lengths do not form a triangle.

Step3: Check the second option (\(a = 6\), \(b = 9\), \(c = 15\))

\(6 + 9=15\), and \(15 = 15\). Since \(a + b\) is not greater than \(c\), these side - lengths do not form a triangle.

Step4: Check the third option (\(a = 6\), \(b = 9\), \(c = 16\))

\(6+9 = 15\), and \(15<16\). So, these side - lengths do not form a triangle.

Step5: Check the fourth option (\(a = 8\), \(b = 9\), \(c = 16\))

\(8+9=17\), and \(17>16\).

Answer:

Side \(=16\) cm, side \(=9\) cm, side \(=8\) cm