The perimeter of the rectangle is 68, and the radius of the circumscribed circle around it is 13. Determine the area of the rectangle.

From the condition it is known that the perimeter of the rectangle is 68, and the radius of the circle that is described around it is 13.
To calculate the area of a rectangle, apply the formula:
S = a * b;
It is known that the sum of the two sides is 34.
Diagonal of a rectangle is the diameter of the circumscribed circle.
Circle diameter (diagonal length) = 2 * 13 = 26.
Let’s compose a system of equations when a and b are the sides of the rectangle:
a + b = 34;
a ^ 2 + b ^ 2 = 26 ^ 2;
We add the two equations of the system and get:
a ^ 2 + b ^ 2 + 2 * a * b = 34 ^ 2;
(a + b) ^ 2 = 34 ^ 2;
S = a * b = (34 ^ 2 – 26 ^ 2) / 2 = 240 sq. units.