Question

question
which of the following sets of numbers could not represent the three sides of a triangle?
answer
{7,10,15} {4,15,21}
{7,17,23} {4,19,20}

Explanation:

Step1: Recall Triangle Inequality Theorem

The triangle inequality theorem states that for three side lengths \(a\), \(b\), and \(c\) (where \(c\) is the longest side), the sum of the two shorter sides must be greater than the longest side, i.e., \(a + b>c\).

Step2: Check \(\{7, 10, 15\}\)

Longest side is \(15\). Sum of shorter sides: \(7 + 10=17\). Since \(17>15\), this can form a triangle.

Step3: Check \(\{4, 15, 21\}\)

Longest side is \(21\). Sum of shorter sides: \(4+15 = 19\). Since \(19<21\), this cannot form a triangle.

Step4: Check \(\{7, 17, 23\}\)

Longest side is \(23\). Sum of shorter sides: \(7 + 17=24\). Since \(24>23\), this can form a triangle.

Step5: Check \(\{4, 19, 20\}\)

Longest side is \(20\). Sum of shorter sides: \(4+19 = 23\). Since \(23>20\), this can form a triangle.

Answer:

\(\{4, 15, 21\}\)