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Answer to Question #2871 in Calculus for Andrew

Question #2871
A manger wants to install a rectangular notice board, ABCD, with area 1600cm^2, in the office meeting room. The notice board is to be subdivided by two thin strips of red tape AC and PQ, where PQ is parallel to AB, the shorter side of the rectangle. The length of red tape is to be a minimum. Determine the dimmensions of the notice board.
Expert's answer
As PQ is parallel to AB,
PQ = AB,
AC2 = AB2 + BC2
as the area of the rectangular is 1600 cm2, AB*BC = 1600, therefore, BC = 1600/AB.
The length of red tape is
L = PQ + AC = AB + (AB2 + 16002/AB2)1/2 = AB + (AB4 + 16002) 1/2 / AB
Let's find the derivative and assume that it is equal to zero:
dL/ d AB = (2 x2)/sqrt(x4+1600) - sqrt(x4+2560000)/x2 + 1 = 0
the positive root of this equation is 40/31/4, thus AB = 40/31/4, BC = 1600/ AB = 40*31/4.

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