Question

which of the following sets of numbers could not be the lengths of the sides of a triangle? 23, 20, 1 21, 13, 20 11, 23, 20 29, 11, 20

Explanation:

Step1: Triangle inequality theorem

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

Step2: Check each set

• Set \(23,20,1\):

Let \(a = 1\), \(b = 20\), \(c = 23\). Then \(a + b=1 + 20=21>23\) (False).

• Set \(21,13,20\):

Let \(a = 13\), \(b = 20\), \(c = 21\). Then \(a + b=13+20 = 33>21\).

• Set \(11,23,20\):

Let \(a = 11\), \(b = 20\), \(c = 23\). Then \(a + b=11 + 20=31>23\).

• Set \(29,11,20\):

Let \(a = 11\), \(b = 20\), \(c = 29\). Then \(a + b=11+20 = 31>29\).

Answer:

\(23,20,1\)