document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #806978 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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A rectangle is inscribed in a circle of radius R/3.
\n" ); document.write( " Express the perimeter of the rectangle as a function of its width.
\n" ); document.write( " Answer will have constant R in it and make sure to use function notation.
\n" ); document.write( ":
\n" ); document.write( "The diagonal of the rectangle = the diameter of the circle, therefore:
\n" ); document.write( " $\"%282R%29%2F3\"$ is the diagonal
\n" ); document.write( ":
\n" ); document.write( "Let L = the length of the rectangle
\n" ); document.write( "and
\n" ); document.write( "Let w = the width
\n" ); document.write( "Pythag
\n" ); document.write( "L^2 + w^2 = $\"%28%282R%29%2F3%29%5E2\"$
\n" ); document.write( "L^2 = $\"%28%282R%29%2F3%29%5E2\"$ - w^2
\n" ); document.write( "L^2 = $\"%28%284R%5E2%29%2F9%29\"$ - w^2
\n" ); document.write( "L = $\"sqrt%28%284R%5E2%29%2F9+-+w%5E2%29\"$
\n" ); document.write( ":
\n" ); document.write( "P = 2L + 2w
\n" ); document.write( "Replace L
\n" ); document.write( "P(w) = $\"2%2Asqrt%28%284R%5E2%29%2F9+-+w%5E2%29\"$ + 2w, is the perimeter in terms of w \n" ); document.write( "

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