Isosceles triangle rde, is a right triangle. what is the measure of the base?

A triangle has six parts . . . 3 angles and 3 sides.  

You've told us the value of exactly one of them . . . one of the angles ... and you've told us that the two legs of the triangle are equal.

That's not enough information to tell what any of the other parts is.

All we can tell is that the angles are 45°, 45°, and 90°, and that the third side is longer than the two equal sides.

We don't have enough information to find the length of anything.  Using the given information, the base could be a millimeter, a parsec, or anything less, in between, or more.  We can't tell.