Question

Which of the following three numbers cannot measure of the sides of a triangle?a. 10, 12, 8b. 7, 12, 11c. 9, 9, 9d. 11,6, 3

Answer 1

The condition on the sides of a triangle is that the sum of any two side lengths must be greater than the third side.

So, if there is any pair of numbers that sum up to less than the third number, those three numbers cannot be measures of the sides of a triangle.

Notice that, for the three numbers given in option d (11, 6, 3), we have:

11 + 6 > 3

11 + 3 > 6

but

6 + 3 = 9

6 + 3 < 11

Therefore, those numbers in option d cannot be measures of the sides of a triangle.