Question 158102
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?
<pre><font size = 4 color = "indigo"><b>
Let the lengths of the legs be {{{N}}}

{{{drawing(400,400,-3,3,-1,4, 
graph(400,400,15,20,15,20),
triangle(-1,0,1,0,0,sqrt(7)),
locate(-.7,1.3,N),locate(.6,1.3,N) 
locate(-.15,-.1,N/2)
 )}}}

{{{Perimeter = P}}}

{{{P = N+N+N/2}}}

the perimeter is between 6 and 16 units

{{{6<P<16}}}

{{{6<N+N+N/2<16}}}

Multiply all three side by 2

{{{2(6)<2(N+N+N/2)<2(16)}}}

{{{12<2N+2N+N<32}}}

{{{12<5N<32}}}

Divide all three sides by 5:

{{{12/5<(5N)/5<32/5}}}

{{{2.4<N<6.4}}}

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

{{{matrix(1,9,"{",3,",",4,",",5,",",6,"}")}}}

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</pre>