Question

33 which of the following sets of lengths can not form a triangle? a 9,14,24 b 3,4,5 c 18,13,12 d 9,17,9

Explanation:

Step1: Recall Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. For a triangle with side lengths \(a\), \(b\), and \(c\) (where \(c\) is the longest side), the inequality \(a + b>c\) must hold.

Step2: Check Option A

For sides \(9\), \(14\), \(24\) (longest side \(24\)):
Calculate \(9 + 14 = 23\).
Compare \(23\) with \(24\): \(23<24\). So, this does not satisfy the triangle inequality.

Step3: Check Option B (for verification)

For sides \(3\), \(4\), \(5\) (longest side \(5\)):
\(3 + 4 = 7>5\), \(3 + 5 = 8>4\), \(4 + 5 = 9>3\). Satisfies the inequality.

Step4: Check Option C (for verification)

For sides \(18\), \(13\), \(12\) (longest side \(18\)):
\(13 + 12 = 25>18\), \(13 + 18 = 31>12\), \(12 + 18 = 30>13\). Satisfies the inequality.

Step5: Check Option D (for verification)

For sides \(9\), \(17\), \(9\) (longest side \(17\)):
\(9 + 9 = 18>17\), \(9 + 17 = 26>9\), \(9 + 17 = 26>9\). Satisfies the inequality.

Answer:

A. \(9, 14, 24\)