SOLUTION: A rectangle is inscribed in a circle of radius R/3. Express the perimeter of the rectangle as a function of its width. Answer will have constant R in it and make sure to use functi

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Question 1177809: A rectangle is inscribed in a circle of radius R/3. Express the perimeter of the rectangle as a function of its width. Answer will have constant R in it and make sure to use function notation.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A rectangle is inscribed in a circle of radius R/3.
Express the perimeter of the rectangle as a function of its width.
Answer will have constant R in it and make sure to use function notation.
:
The diagonal of the rectangle = the diameter of the circle, therefore:
%282R%29%2F3 is the diagonal
:
Let L = the length of the rectangle
and
Let w = the width
Pythag
L^2 + w^2 = %28%282R%29%2F3%29%5E2
L^2 = %28%282R%29%2F3%29%5E2 - w^2
L^2 = %28%284R%5E2%29%2F9%29 - w^2
L = sqrt%28%284R%5E2%29%2F9+-+w%5E2%29
:
P = 2L + 2w
Replace L
P(w) = 2%2Asqrt%28%284R%5E2%29%2F9+-+w%5E2%29 + 2w, is the perimeter in terms of w