Answer to Question #2871 in Calculus for Andrew
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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