A farmer makes a rectangular enclosure for his animals. He uses a wall for one side and a total of 72 metres of fencing for the other

Question

A farmer makes a rectangular enclosure for his animals.
He uses a wall for one side and a total of 72 metres of fencing for the other three sides.
The enclosure has width x metres and area A square metres.
Show that A = 72x – 21.

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Hải Đăng 3 years 2021-08-15T19:59:33+00:00 1 Answers 264 views 0

Answers ( )

  1. Sigrid
    1
    2021-08-15T20:01:02+00:00
    Reply

    Answer:

    Remember that, for a rectangle of length L and width W, the area is:

    A  =L*W

    And the perimeter is:

    P = 2*(L + W)

    In this case, we know that:

    W = x

    Let’s assume that one of the “length” sides is on the part where the farmer uses the wall.

    Then the farmer has 72 m of fencing for the other “length” side and for the 2 wide sides, then:

    72m = L + 2*x

    isolating L we get:

    L = (2x – 72m)

    Then we can write the area of the rectangle as:

    A = L*x = (2x – 72m)*x

    A = 2*x^2 – 72m*x

    (you wrote  A = 72x – 21, I assume that it is incorrect, as the area should be a quadratic equation of x)

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