Question

do the following side lengths create a triangle? 20, 10, 9 options: no clue, no, yes, sometimes

Explanation:

Step1: Recall Triangle Inequality Theorem

For three side lengths \(a\), \(b\), \(c\) to form a triangle, the sum of any two sides must be greater than the third side. So we need to check three inequalities: \(a + b>c\), \(a + c>b\), and \(b + c>a\).

Step2: Identify the sides

Let \(a = 20\), \(b = 10\), \(c = 9\).

Step3: Check \(a + b>c\)

Calculate \(a + b=20 + 10 = 30\). Since \(30>9\), this inequality holds.

Step4: Check \(a + c>b\)

Calculate \(a + c = 20+9 = 29\). Since \(29>10\), this inequality holds.

Step5: Check \(b + c>a\)

Calculate \(b + c=10 + 9 = 19\). Now, compare \(19\) with \(a = 20\). Since \(19<20\), this inequality does not hold.

Answer:

B. No