Question

If the lengths of two sides of a triangle are 5 and 9, respectively, which of the following could be the length of the third side of the triangle? Indicate all such lengths. [A] 3 [B] 5 [G] 8 [D] 15

Answer 1

There are two answers:

B) 5

C) 8

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Explanation:

If we had a triangle with sides a, b and c, then we can say

b-a < c < b+a

where b is larger than 'a'. This is the triangle inequality theorem

In this case, a = 5 and b = 9 so,

b-a < c < b+a

9-5 < c < 9+5

4 < c < 14

Telling us that c is some number between 4 and 14, not including either endpoint. If c is a whole number, then c could be any value from this set: {5,6,7,8,9,10,11,12,13}

We see that the numbers 5 and 8 are in this set. The values 3 and 15 are not in the set.