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.
:
The diagonal of the rectangle = the diameter of the circle, therefore:
{{{(2R)/3}}} is the diagonal
:
Let L = the length of the rectangle
and
Let w = the width
Pythag
L^2 + w^2 = {{{((2R)/3)^2}}}
L^2 = {{{((2R)/3)^2}}} - w^2
L^2 = {{{((4R^2)/9)}}} - w^2
L = {{{sqrt((4R^2)/9 - w^2)}}}
:
P = 2L + 2w
Replace L
P(w) = {{{2*sqrt((4R^2)/9 - w^2)}}} + 2w, is the perimeter in terms of w