Question

answer
which of the following sets of numbers could represent the three sides of a triangle?
{11,25,37}
{15,27,42}
{12,25,37}
{4,19,21}
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Explanation:

Step1: Apply triangle inequality theorem

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

For \(\{11,25,37\}\)

Let \(a = 11\), \(b = 25\), \(c=37\). Then \(a + b=11 + 25=36\). Since \(36<37\), this set does not form a triangle.

For \(\{12,25,37\}\)

Let \(a = 12\), \(b = 25\), \(c = 37\). Then \(a + b=12+25 = 37\). Since \(a + b=c\) (not \(a + b>c\)), this set does not form a triangle.

For \(\{4,19,21\}\)

Let \(a = 4\), \(b = 19\), \(c = 21\). Then \(a + b=4 + 19=23\). Since \(23>21\), \(a + c=4+21 = 25>19\), and \(b + c=19 + 21=40>4\), this set forms a triangle.

For \(\{15,27,42\}\)

Let \(a = 15\), \(b = 27\), \(c = 42\). Then \(a + b=15+27 = 42\). Since \(a + b=c\) (not \(a + b>c\)), this set does not form a triangle.

Answer:

\(\{4,19,21\}\)