SOLUTION: A circle is inscribed in a square. If the area is the circle is 36π sq. in, what is the perimeter of the square in inches??

Algebra ->  Triangles -> SOLUTION: A circle is inscribed in a square. If the area is the circle is 36π sq. in, what is the perimeter of the square in inches??      Log On


   

Question 1141717: A circle is inscribed in a square. If the area is the circle is 36π sq. in, what is the perimeter of the square in inches??
Found 2 solutions by ikleyn, math_helper:
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

pi%2Ar%5E2 = 36%2Api


is the area of the circle - hence, its radius  r = 6.


Then the side of the square is  2*6 = 12 inches and the perimeter of the square is 4 times 12 inches, i.e. 48 inches.    ANSWER


Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
Here are the steps: I encourage you to try it on your own:

You know the area of the circle, and that is +pi%2Ar%5E2+
So +pi%2Ar%5E2+=+36pi+ == (dividing both sides by pi) ==> +r%5E2+=+36+

You can find r by taking the square root.

Now envision the circle in the square, how long is one side of the square, in terms of the radius of the circle, r ? Hint: there is a simple relationship between length of each side and the radius of the circle.

Since that value is one side, the perimeter is just 4 times that number.