SOLUTION: the problem is.... the lengths of the legs of an isosceles triangle are integers. the base is half as long as each leg. what are the possible lengths of the legs if the perimeter

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Question 158102This question is from textbook algebra and trigonometry structure and method book 2
: the problem is....
the lengths of the legs of an isosceles triangle are integers. the base is half as long as each leg. what are the possible lengths of the legs if the perimeter is between 6 and 16 units? This question is from textbook algebra and trigonometry structure and method book 2

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
the problem is....
the lengths of the legs of an isosceles triangle are integers. the base is half as long as each leg. what are the possible lengths of the legs if the perimeter is between 6 and 16 units?

Let the lengths of the legs be N



Perimeter+=+P

P+=+N%2BN%2BN%2F2

the perimeter is between 6 and 16 units

6%3CP%3C16

6%3CN%2BN%2BN%2F2%3C16

Multiply all three side by 2

2%286%29%3C2%28N%2BN%2BN%2F2%29%3C2%2816%29

12%3C2N%2B2N%2BN%3C32

12%3C5N%3C32

Divide all three sides by 5:

12%2F5%3C%285N%29%2F5%3C32%2F5

2.4%3CN%3C6.4

The only integers N between 2.4 and 6.4, for
the legs are 



We aren't told that the base has to be an integer, 
too. If it had to be an integer too we would have to 
discard the odd integers for the legs.  But since we 
are not told that the base must be an integer, too,
we will stick with the above answer.

Edwin