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It is the possible to design a rectangular park Of perimeter 80m and area 400msq ? If so find its length and breadth

    • Posted by Vivek Pandey 4 years, 9 months ago

    CBSE > Class 10 > Mathematics
    • 2 answers

    Vivek Pandey 4 years, 9 months ago

    Thank you very much

    0Thank You

    Yogita Ingle 4 years, 9 months ago

    Let the length and breadth of the park be l and b.
    Perimeter = 2 (l + b) = 80
    l + b = 40
    Or, b = 40 - l
    Area = l×b = l(40 - l) = 40l - l240l -  l2 = 400
    l2 -  40l + 400 = 0
    Comparing this equation with al2 + bl + c = 0, we get
    a = 1, b = -40, c = 400
    Discriminant = b2 - 4ac
    (-40)2 - 4 × 400
    = 1600 - 1600 = 0
    b2 - 4ac = 0
    Therefore, this equation has equal real roots. And hence, this situation is possible.
    Root of this equation,l = -b/2a
    l = (40)/2(1) = 40/2 = 20
    Therefore, length of park, l = 20 m
    And breadth of park, b = 40 - l = 40 - 20 = 20 m.

    1Thank You

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