What are the equal sides lengths of an isosceles triangle with base 16?

What are the equal sides lengths of an isosceles triangle with base 16?

I feel like there is some information missing. Is there a way to do this problem?

Context

I teach math and someone is asking me this over the internet; I feel you would need to know an angle, height, perimeter, or area to figure this out.

• Yes you'd need to know an angle – Gregory Grant Mar 10 '15 at 1:38
• Or an altitude or area or circumradius or some other property that distinguishes a $16,9,9$ triangle from a $16,10,10$ triangle. – David K Mar 10 '15 at 1:42
• Thank you! I teach math and someone is asking me this over the internet and I feel you would need to know an angle, height, perimeter, or area to figure this out. Thanks for confirming I'm not crazy. :) – Joy Mar 10 '15 at 1:43
• One thing you can say is that the length of each leg has to exceed $8$ in order to satisfy the Triangle Inequality. – N. F. Taussig Mar 10 '15 at 2:37

I assume that you intend the base to be not one of the sides of equal length.

Each of the remaining side lengths should be greater than 8 units long for a triangle to exist. Other than that, there are an infinite number of possible solutions if no angle in the triangle is specified.

• As mentioned in the comments to the original post, the additional information need not be an angle. It could be a height, perimeter, area, or something else. – Joel Reyes Noche Mar 10 '15 at 1:58