SOLUTION: What is the radius of the smallest circle that surrounds a 5-by-12 rectangle?

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Question 1154417: What is the radius of the smallest circle that surrounds a 5-by-12 rectangle?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The diagonals of the rectangle will be diameters of the smallest circle that surrounds the rectangle.

By the Pythagorean Theorem, the diagonal of this rectangle is 13.

So the diameter of the circle is 13, making its radius 6.5.

ANSWER: 6.5
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

The smallest circle that surrounds any rectangle ("a rectangle"), is called circumscribed circle around the rectangle.



For any such a rectangle and circumscribed circle, its center lies in the intersection point of the rectangle's diagonals,

and each of the two diagonals is a diameter of the circle.



The diagonal (each diagonal) of a 5-by-12 rectangle has the length of 13 units

(13^2 = 5^2 + 12^2).


The radius of this circle is half of the diagonal length.


Therefore, the radius of such circle is   = 6.5 units.

Answered, solved, and explained.

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