Question

which of the following sets of numbers could not be the lengths of the sides of a triangle? 5, 20, 22 10, 6, 18 23, 21, 14 4, 25, 22

Explanation:

Step1: Check triangle inequality for \(5,20,22\)

Check \(5 + 20>22\) (\(25>22\)), \(5+22 > 20\) (\(27>20\)), \(20 + 22>5\) (\(42>5\))

Step2: Check triangle inequality for \(10,6,18\)

Check \(10+6>18\). \(10 + 6=16<18\)

Step3: Check triangle inequality for \(23,21,14\)

Check \(23+21>14\) (\(44>14\)), \(23 + 14>21\) (\(37>21\)), \(21+14>23\) (\(35>23\))

Step4: Check triangle inequality for \(4,25,22\)

Check \(4+22>25\). \(4+22 = 26>25\), \(4+25>22\) (\(29>22\)), \(22+25>4\) (\(47>4\))

Answer:

\(10,6,18\)