SOLUTION: SUPER URGENT!! What is the radius of the smallest circle that surrounds a 5-by-12 rectangle? So far I've figured out that the diameter of the circle needs to be greater than 12 (t

Algebra ->  Circles -> SOLUTION: SUPER URGENT!! What is the radius of the smallest circle that surrounds a 5-by-12 rectangle? So far I've figured out that the diameter of the circle needs to be greater than 12 (t      Log On


   

Question 963976: SUPER URGENT!! What is the radius of the smallest circle that surrounds a 5-by-12 rectangle?
So far I've figured out that the diameter of the circle needs to be greater than 12 (the width of the rectangle), and the area of the circle needs to be greater than 60 (the area of the rectangle). I'm stumped. Help??
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Imagine drawing a circle on a cartesian system, centered at the origin, and sketch a rectangle whose diagonals will intersect at the center of the circle. Each of these diagonals is also a diameter of the circle. You want to find the length value of this diagonal (either of them, since one will be same size as the other).

Understand that a diagonal cuts the rectangle into two congruent right triangles.

d=sqrt%285%5E2%2B12%5E2%29
d=sqrt%2825%2B144%29
d=sqrt%28169%29
highlight_green%28d=13%29, the diagonal or the diameter of the circle.

The radius value is highlight%2813%2F2=6%261%2F2%29.