I do not know what your math level is but I am going to keep its as simple as possible. You said that when you form squares and the sides and add them you get the square of the third side, thus, in algebraic terms,
- but this is the Pythagorean Theorem. Thus, we must have a right triangle. Now you said that it is isoseles. Thus, two sides are equal. Thus, two of the angles must also be equal. Since one angle is already 90 degrees the other two angles must add up to 90 degrees also because the sum of the angles of ANY triangle is 180. Thus, the other two angles must be 45 and 45. Finally, there is a theorem about a 45-45-90 triangle that says if the smaller sides are
then the biggest side (hypotenuse) is