A triangle has two sides with the lengths 7 and 6 . What are the possible lengths of the third side? Use the triangle Inequality Theorem .

Question

anonymous · Answer

@april115 @MathLegend @sohokpop @almartinez26 @chevyguy Help ?

yttrium · Answer

Please be reminded that triangle inequality statement states that in any triangle, the sum of its two sides must always be greater than the third side. Mathematically,
if we have a triangle ABC with sides a, b and c. The third side, say c, is given by:
$$c \le a+b$$

yttrium · Answer

*i mean always greater than of equal. Hope you get what I mean @Faith_Rochelle

yttrium · Answer

So say we let a = 7 and b = 6 and we are finding for c, what should be it's possible values now?

anonymous · Answer

I came up with these equations :
 6+7 > x
7 + x > 6 
x+6 > 7

anonymous · Answer

@Yttrium

yttrium · Answer

Great. Just get the most general equation, and that is the 1st one. With that, we can solve now for all values of x's

anonymous · Answer

|dw:1383967105984:dw|

yttrium · Answer

Actually, we can just say that 
$$x \le 13$$

since there is really no negative dimensions.

anonymous · Answer

if the angle between the lengths infinitely approaches 0 degrees, the 3rd side will infinitely approach 1, not zero.

Am I missing something?

ranga · Answer

when x = 13 there will be no triangle  nor when x = 0.

ranga · Answer

So the end points 0 and 13 should be excluded.

anonymous · Answer

bot 0.5 should be exclused, as well as 0.6, and 1 for that matter.

anonymous · Answer

1.00000000001 is legal, 1 is not.

anonymous · Answer

1<x<13 unless someone can point out my error.

ranga · Answer

you may be right about 1.

anonymous · Answer

picture the two vertices approaching each other spaced apart by 1, they can only get so close to each other.

anonymous · Answer

@ehuman I agree with your answer . so if I was asked for two possible side lengths I could say 14 and 15 are two possible side lengths. ?

anonymous · Answer

all legal possible lengths for the third side are all real numbers greater than 1 and less than 13

anonymous · Answer

Oh okay !! Thank you (:

anonymous · Answer

14 and 15 are impossible side lengths for a triangle with sides 6 and 7

ranga · Answer

When the angle approaches 0, the third side will approach the difference of the other two sides.  When the angle approaches 180, the third side will approach the sum of the other two sides.    Hence      7 - 6 <   x   < 7 + 6     or   1 < x < 13