SOLUTION: 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 units

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Question 338579: 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 units and 16 units?
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
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 units and 16 units?
Let the base by x.  Then since the base is half as long as each leg,

each leg is twice as long as the base, or 2x

Then the perimeter P is given by

Perimeter = base + leg + leg

P = x + 2x + 2x

P = 5x

We are told that

6 < P < 16

Substituting 5x for P

6 < 5x < 16





The only integers between those numbers are 2 and 3.

So the possible length of the base is either 2 or 3.  That makes
the possible lengths of the legs, which are twice as long as the base, 
be either 4 or 6.

Answer: 4, 6

Edwin
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