How many different isosceles triangles have integer side lengths and perimeter 23?

Guest Dec 21, 2018

#1**+1 **

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

CPhill Dec 21, 2018