The sides of the rectangle are 10 and 24. Find the radius of the circle circumscribed about this rectangle.

From the condition it is known that the sides of the rectangle are equal to 10 and 24. In order to find the radius of the circle circumscribed about the rectangle, remember that the diagonal is equal to the radius of the circumscribed circle, and the radius will be equal to half the diagonal. Diagonal of a rectangle Consider a right-angled triangle formed by the sides of the rectangle and the diagonal.

The sides of the rectangle are the legs of a right-angled triangle, and the diagonal of the rectangle is the hypotenuse.

To find the hypotenuse, we will use the Pythagorean theorem.

The sum of the squares of the legs is equal to the square of the hypotenuse.

a ^ 2 + b ^ 2 = c ^ 2;

10 ^ 2 + 24 ^ 2 = ^ c2;

100 + 576 = c ^ 2;

c ^ 2 = 676;

c = 26 diagonal of the rectangle.

The radius of the circumscribed circle is 26/2 = 13.