text: L*w = 50, so w = 50/L = 50*L^(-1)\n\nWe're optimizing the Printed area: P = (L-2)(w-1)\n\nReplacing w,\n\nP = (L-2)(50L^(-1) - 1)\nMultiplying:\nP = 50 -100L^(-1) - L + 2 = 52 - 100L^(-1) - L\n\nP' = 100L^(-2) - 1\nP' = 100/(L^2) - 1 = (100-L^2)/L^2\n\nSet P' = 0, you get L = 10 (or -10, which you disregard)\n\nSo the length of the page is 10 in, and the width must be 5 inches to get area of 50 sq. inches