SOLUTION: if the perimeter of a triangle is 18 then the length of one of the sides cannot be The options in the answer are: a-1 ,b-3.c-6 ,d-8 ,e-9

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Question 435822: if the perimeter of a triangle is 18 then the length of one of the sides cannot be
The options in the answer are:
a-1 ,b-3.c-6 ,d-8 ,e-9
Found 2 solutions by ewatrrr, richard1234:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi





P=  2L + 2W = 18 where L is the length and W is the width

P is the Perimeter, the distance 'ALL'away around the rectangle...

OR L + W = 9

THAT IS: the length of one of the sides cannot be 9

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Whoops, wasn't thinking properly. The other tutor stated 9 cannot be a possible side length for a triangle. This is correct, but for a completely different reason.

Suppose a,b,c are the lengths of the triangle with a+%3C=+b+%3C=+c, and a%2Bb%2Bc+=+18. By the triangle inequality, a%2Bb+%3E+c. Adding c to both sides, a%2Bb%2Bc+%3E+2c. Since a+b+c = 18, 18+%3E+2c, 9+%3E+c, hence c must be less than 9, so 9 cannot be a side length.