Which three lengths can NOT be the side lengths of a triangle?

A. 2, 8, 8

B. 2, 3, 6

C. 4, 5, 7

D. 5, 6, 9

KaylaDoodlez May 22, 2017

#1**+2 **

B; 2,3,6

To solve this problem, you must understand a relationship about triangles: the length of two smaller legs must be greater than the longest leg. in other words,

\(Leg_1+Leg_2>Leg_3\)

If this condition is false, a triangle cannot exist because a side length is too long.

Let's see if A is the correct answer:

First, identify which leg is the longest. In this case, there are two legs with length 8. That is OK. Only one of them can be substituted in for Leg3.

\(2+8>8\)

\(10>8\)

True. This statement is true. Because this is true, that means that a triangle can have the side lengths of length 2,8, and 8.

Let's see if B is the correct answer:

\(2+3>6 \)

\(5>6\)

False. As aforementioned, if the statement is false, then a triangle cannot exist with the given side lengths. This is the correct answer. For fun, let's try the other answer choices anyway! Let's test out C:

\(4+5>7\)

\(9>7\)

9>7 is a true statement, so a triangle can exist.

And finally, D:

\(5+6>9\)

\(11>9\)

Yes, a triangle can exist with these parameters, too. Therefore, B is the only correct answer.

TheXSquaredFactor May 22, 2017