Question

Which of the following sets of numbers can be used as the lengths of the sides of a triangle ?

Accepted Answer

B. By triangle inequality, the sum of any two sides must be strictly greater than the third side. - $[5, 7, 12]$: $5 + 7 = 12 
gtr 12$ - $[5, 7, 9]$: $5 + 7 = 12 > 9$, $5 + 9 = 14 > 7$, $7 + 9 = 16 > 5$ (Valid) - $[7, 9, 17]$: $7 + 9 = 16 
gtr 17$ - $[2, 4, 10]$: $2 + 4 = 6 
gtr 10$

Valid triangle side lengths

Explanation

Practise this under exam conditions