Which set of numbers could NOT represent the three sides of a triangle?

Question

Which set of numbers could NOT represent the three sides of a triangle?

a	4,5,6
b	5,10,15
c	5,12,15
d	30,40,50

Answer 1

In a valid triangle, the length of any side must be less than the sum of the lengths of the other two sides.

therefore the length of the longest side must be less than the sum of the lengths of the other two sides

for a, the biggest side (6) is less than 4 + 5 = 9, so that is valid

for b, the biggest side (15) is NOT less than 5 + 10 = 15, so that is invalid

for c, the biggest side (15) is less than 5 + 12 = 17, so that is valid

for d, the biggest side (50) is less than 30 + 40 = 70, so that is valid

Answer 2

Any two sides added together has to be more than the third side.

4 + 5 = 9 and 9 > 6

4 + 6 = 10 and 10 > 5

5 + 6 = 11 and 11 > 5

So, a could be a triangle. Keep going.

Answer 3

If sides of triangle is a, b, c, then must be true triangle inequality: a < b + c, b < a + c, c < a + b.

We see that for case b 5, 10, 15: 15 = 5 + 10 and this contradict with inequality.