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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

Best Answer 

 #4
avatar
+1

Just imagine a triangle with two arms that don't meet... that is what would happen if the two sides were less long than the base.

Guest May 22, 2017
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4+0 Answers

 #1
avatar+815 
+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
 #3
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Thank you!!!!

KaylaDoodlez  May 22, 2017
 #2
avatar+89843 
+1

Hint,

 

Try drawing a triangle with sides   7cm, 2cm and 3cm

Make the base 7 cm long.

 

Actually draw this on a peice of paper and see if you can do it, or try to work out why you can't do it :)

Melody  May 22, 2017
 #4
avatar
+1
Best Answer

Just imagine a triangle with two arms that don't meet... that is what would happen if the two sides were less long than the base.

Guest May 22, 2017

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