The owner of a motel has 2900 m of fencing and wants to enclose a rectangular plot of land that borders a straight highway. If she does not

Question

The owner of a motel has 2900 m of fencing and wants to enclose a rectangular plot of land that borders a straight highway. If she does not fence the side along the highway, what is the largest area that can be enclosed?

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Alaia 1 month 2021-10-20T20:36:59+00:00 1 Answer 0 views 0

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    2021-10-20T20:38:06+00:00

    Answer:

    Step-by-step explanation:

    Given that the owner of a motel has 2900 m of fencing and wants to enclose a rectangular plot of land that borders a straight highway.

    Fencing is used for 2times length and 1 width if highway side is taken as width

    So we have 2l+w = 2900

    Or w = 2900-2l

    Area of the rectangular region = lw

    A(l) = l(2900-2l) = 2900l-2l^2\\

    Use derivative test to find the maximum

    A'(l) = 2900-4l\\A"(l) = -4<0

    So maximum when I derivative =0

    i.e when l =\frac{2900}{4} =725

    Largest area = A(725)

    = 725(2900-2*725)\\= 1051250

    1051250 sqm is area maximum

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