You can put this solution on YOUR website! If the side lengths do not have to be all integers, the answer is an obvious yes (this is because we can scale some triangle by any scale factor).
If the side lengths have to all be integers, the answer is still yes (consider an isosceles triangle consisting of two 3-4-5 right triangles, or an isosceles triangle with two 5-12-13's). Hence it follows that there are infinitely many such triangles.
