What is the circumference of a circle circumscribed around a rectangle with sides 10 cm and 24 cm?

81.7 cm

Step-by-step explanation:

Best that you draw both circle and rectangle.  The center of the rectangle coincides with the center of the circle.  From this center draw a vertical line segment to the upper edge of the rectangle.  Similarly, draw a horiz. line to the right edge.  The length of this vertical line segment will be half of 10 cm, or 5 cm; the length of this horiz. line segment will be half of 24 cm, or 12 cm.

Draw a diagonal from the center to the far corner (vertex) of the rectangle.  Using the Pythagorean Theorem, we determine that the length of this diagonal is d = √(5^2 + 12^2) = 13.  This is also the radius of the circle.

The circumference of the circle is thus C = 2πr, or C = 2π(13 cm), or

26π cm, or roughly 81.7 cm