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30 January, 19:18

Diana has available 80 yards of fencing and wishes to enclose a rectangular area. (a) Express the area A of the rectangle as a function of the width W of the rectangle. (b) For what value of W is the area largest? (c) What is the maximum area?

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  1. S
    30 January, 20:44
    0
    a) A = 40*W - W^2

    b) W = 20

    c) A = 400

    Step-by-step explanation:

    a) Let be

    W = width W of the rectangle

    L = lenght of the rectangle

    P = Perimeter of the rectangle

    A = area of the rectangle

    P = 2*L + 2*W

    80 = 2*L + 2*W

    So, 2*L = 80 - 2*W

    L = 40 - W

    A = L * W

    Replacing L

    A = (40 - W) * W

    A = 40*W - W^2

    b) To find the máximum value for W, we derivate area and equal to zero

    A' = 40 - 2*W

    40 - 2*W = 0

    2*W = 40

    W = 20

    c) With the value for W, we find L

    L = 40 - W

    L = 40 - 20

    L = 20

    A = W*L

    A = 20 * 20

    A = 400
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