Question

a wire 36 meter long is cut into two pieces. each piece is bent to form a rectangle which is 1 cm longer than its width. How long should each piece be to minimize the sum of the areas of the two rectangle?

Answer 1

width of each rectangle = x
length of each rectangle = x+1

sum of area = 2x(x+1) = 2x^2 + 2x
d(area)/dx = 4x + 2
= 0 for a max/min

4x + 2 = 0
4x = -2
x = -1/2

also 2(2x + 2(x+1)) = 36
4x + 4x + 4 = 36
8x=32
x=4

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