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

Algebra.Com
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(20054)   (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
RELATED QUESTIONS

the problem is.... the lengths of the legs of an isosceles triangle are integers. the... (answered by Edwin McCravy)
The lengths of the legs of an isosceles triangle are integers. The base is half as long... (answered by stanbon)
the base of an isosceles triangle and one of its legs have lengths that are consecutive... (answered by checkley71)
What are the angle measures of an isosceles triangle whose base is half as long as its... (answered by Edwin McCravy)
The length of the base of an isosceles triangle is 12 cm. What are the possible lengths... (answered by Alan3354)
The lengths of the legs of an isoceles triangle are integers.The bas is half as long as... (answered by )
the hypotenuse of a right triangle is 10 cm long. one leg is twice as long as the other.... (answered by ewatrrr)
If you have the base of a isosceles right triangle as 12 feet, what are the other two leg (answered by richwmiller)
The length of the base of an isosceles triangle is 16. What is the range of possible... (answered by josgarithmetic)