In a rectangle, one side is 2 cm and the other is 9 cm less than the diagonal. Find S of the rectangle.

Let the diagonal Xcm, then the unknown side is equal to X – 9. By the Pythagorean theorem, you can find X, from the equation (where the diagonal of the rectangle is the hypotenuse of the triangle, and the sides of the rectangle are the legs):
X ^ 2 = (X – 9) ^ 2 + 2 ^ 2, X ^ 2 = X ^ 2 – 18X + 81 + 4, X = 85/18.
The area of the rectangle S = 2 * 85/18 = 85/9 = 9 * 4/9 cm ^ 2.