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9 January, 07:35

The owner of the Rancho Bar X wishes to use 2400 yards of fencing to enclose a rectangular piece of grazing land along the straight portion of a river and then subdivide it into two parts by means of a piece of fencing perpendicular to the riverbank. No fencing is required along the river. What is the largest area that can be enclosed and what are its dimensions

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  1. 9 January, 07:57
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    Step-by-step explanation:

    Let length be x and breadth be y.

    Along the river no fencing is required so total boundary line of the rectangular land = x + y + y = x + 2y

    add divider to it so total length

    = x + 2y + y = x + 3y

    x + 3y = 2400

    area A = xy

    y (2400 - 3y) = A

    2400y - 3y² = A

    For maximum area dA / dy = 0

    2400 - 6y = 0

    y = 400 yards.

    x = 1200 yards

    largest area = xy

    = 48000 sq yards.
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