anonymous
  • anonymous
A rectangle has an area of 16 square feet. Its length and width are whole numbers. What is its maximum perimeter?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
(L) x (W) = 16 2L + 2W = P Solve for one of the variables, in this case lets solve for (w) LW = 16 W = 16/L plug that in to the Perimeter Eqauation: 2(L) + 2( 16/L ) = P Now take the derivative of P P = 2L + 32/L P'= 2 + 32( -1/L^2 ) Now set P' to 0, because the derivative is 0 at its Maximums and Minimums 0 = 2 - 32/(L^2) -2 = -32/(L^2) -2(L^2) = -32 L^2 = 16 L = 4 Plug this back in to solve for W W = 16/L W = 16/4 W = 4 tada! so the maximum perimeter must be 16, and the dimensions are 4 by 4
experimentX
  • experimentX
4x4, 8x2, 16x1 possibilities
anonymous
  • anonymous
Actually I found the answer to be 34 feet :) But thanks for the help!

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