Question

question 20 of 50
which of the following sets of numbers could be the lengths of the sides of a triangle?
2, 3, 4
12, 11, 1
9, 4, 5
22, 14, 7
15, 9, 5

Explanation:

Step1: Recall Triangle Inequality Theorem

For three side lengths \(a\), \(b\), \(c\) (where \(c\) is the largest), the sum of the two smaller sides must be greater than the largest side: \(a + b>c\).

Step2: Check 2, 3, 4

Largest side is 4. Sum of smaller sides: \(2 + 3=5\). Since \(5>4\), check holds.

Step3: Check 12, 11, 1

Largest side is 12. Sum of smaller sides: \(11 + 1 = 12\). But \(12 = 12\) (needs to be \(>\)), so check fails.

Step4: Check 9, 4, 5

Largest side is 9. Sum of smaller sides: \(4 + 5=9\). \(9 = 9\) (needs to be \(>\)), check fails.

Step5: Check 22, 14, 7

Largest side is 22. Sum of smaller sides: \(14 + 7 = 21\). \(21<22\), check fails.

Step6: Check 15, 9, 5

Largest side is 15. Sum of smaller sides: \(9 + 5 = 14\). \(14<15\), check fails.

Answer:

A. 2, 3, 4