How many isosceles triangles with total side length $100$ are there?

Question

Let the sum of the three sides of a triangle be $100,$ and all the sides are positive integers length, how many possible isosceles triangles are there?

Answer 1

Hint: Let the side length $=x$, then we know the base length $=100-2x$. Then set up your inequality(s).

Answer 2

Hint: We can certainly do $(49,49,2)$, $(48,48,4)$, $(47,47,6)$ and so on for a while. But the sum of the two equal sides cannot be less than or equal to the third side. That should tell you where we need to stop.

Answer 3

x=2*a+100-2*a if (100-2*a)

2*34+32=100 2*35+30=100 2*36+28=100 2*37+26=100 2*38+24=100 2*39+22=100 2*40+20=100 2*41+18=100 2*42+16=100 2*43+14=100 2*44+12=100 2*45+10=100 2*46+8=100 2*47+6=100 2*48+4=100 2*49+2=100 number of solution: 16