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26 June, 14:31

A rectangular garden is fenced on three sides with a wall forming the fourth

The total length of the fence is 30 m. The area of the garden is 100 m². Find the

dimensions of the garden.

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Answers (1)
  1. 26 June, 14:59
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    The dimensions are 5 m by 20 m.

    Step-by-step explanation:

    The area = length * width = 100 m^2.

    2 times the width + the length = 30 m.

    So we have the equations:

    wL = 100

    2w + L = 30

    From the first equation:

    L = 100/w so substituting in the second equation, we have:

    2w + 100/w = 30

    Multiply through by w:

    2w^2 + 100 = 30w

    2w^2 - 30w + 100 = 0 Divide by 2:

    w^2 - 15w + 50 = 0

    (w - 5) (w - 10) =

    w = 5 or 10m.

    So L = 100/5 or 100/10

    = 20 or 10.

    As it is rectangular then w = 5 and L = 20.
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