Question

Which of the following do not represent the measures of the sides of a triangle?

Answer 1

Answer:     B) 43, 133, 89

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Explanation:

For this answer choice, we have p = 43, q = 133, and r = 89. Note how p+r = 43+89 = 132, which is not larger than the third remaining side q = 133. Therefore, p+r > q is false and a triangle cannot be formed.

A triangle is only possible if and only if adding any two sides leads to a sum larger than the third side (triangle inequality theorem).

Put another way, we must have these three conditions hold true for a triangle to form:

• p+q > r
• p+r > q
• q+r > p

If any of those three are false, then we cannot make a triangle with side lengths p,q,r

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Let's go over choice C for an example in which we can form a triangle

p = 5, q = 6, r = 7

We can see that,

• p+q = 5+6 = 11 which is greater than r = 7. So p+q > r is true.
• p+r = 5+7 = 12 which is greater than q = 6. So p+r > q is true.
• q+r = 6+7 = 13 which is greater than p = 5. So q+r > p is true.

All three conditions are true, and therefore we have a triangle that is possible with side lengths p = 5, q = 6, r = 7. I recommend cutting out slips of paper with these lengths to try it out yourself, so you have a real world example to play with. Choices A and D are a similar story to choice C, so we can rule out all three of these choices.

Answer 2

B is the answer to this question