How many different isosceles triangles have integer side lengths and perimeter 23?
Let x be the equal sides of the triangle...let y be the remaining side
One way of solving this is with a graph...
We have these constraints
2x + y = 23
And by the Triangle Inequality, we have
2x > y
x + y > x ⇒ y > 0
Look at the graph of the feasible region here : https://www.desmos.com/calculator/kyzw7wa8v5
It shows that there are six such triangles