SOLUTION: A square, whose area is equal to the perimeter of the rectangle whose value 16, is inscribed in a circle with its four vertices on the circumference of the circle. What is the diam

Algebra ->  Surface-area -> SOLUTION: A square, whose area is equal to the perimeter of the rectangle whose value 16, is inscribed in a circle with its four vertices on the circumference of the circle. What is the diam      Log On


   

Question 935203: A square, whose area is equal to the perimeter of the rectangle whose value 16, is inscribed in a circle with its four vertices on the circumference of the circle. What is the diameter of the circle?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A square, whose area is equal to the perimeter of the rectangle whose value 16, is inscribed in a circle with its four vertices on the circumference of the circle.
What is the diameter of the circle?
:
The square area is given as 16, therefore:
sqrt%2816%29 = 4 is the length of the side of the square
:
The square in the circle: half the square is a right triangle:
Using pythag; a^2 + b^2 = c^2
a = 4
b = 4
c = diameter of the circle
:
c = sqrt%284%5E2+%2B+4%5E2%29
c = 5.656854 is the diameter of the circle