Find the lengths of the three sides of the right triangle with the measurements of one leg square root of x hypotenuse is 6 plus square root of x and the other leg is square root of x plus 63?

I need to get this clearer. You have a right triangle. Call the sides adjacent to the right angle a and b, and the hypotenuse h. Now you are saying:

a = root of x, b = (root x + 63), h = (root x + 6). Is that right?

Now h2 = a2 + b2 , so (root x +6)2 = (root x)2 + (root x + 63)2

Simplifying, we get x + 114rootx +3933 = 0 which is obviously impossible for real numbers. Therefore I think you have made a mistake with the specification. Please reconsider the question.

Addition / Correction:

The square root of x could represent a negative number but then it couldn't be the length of the side of a triangle...