Math, asked by aswanthkumarvk, 1 year ago

there is a path of uniform width outside and around a rectangle garden of discussion 30m×20m area of path I'd 104m square .what is the width of the garden?


kvnmurty: qn is to find the width of the path around the garden... not width of the garden..

Answers

Answered by kvnmurty
5
See the diagram enclosed of the garden and the path around it.

Let the park be of size:  L = 30 m.   B = 20 m.
Let the width of the path be w meters.

Area of the path = 2 * (L+2w) *w + 2 * (B+2w)* w  -  4 w * w
  We subtract 4 w² because the 4 corner squares are added twice in the calculation of the first two terms.

  So 104 m² = 2 (30+2w) w + 2 *(20+2w)w - 4 w²
       104 = 100 w + 4 w²
        w² + 25 w - 26 = 0
        (w - 1)(w + 26) = 0
         w = 1 m       (ignore negative value.

Width of the path = w = 1 m.

=====================  another way

104 = path area = (30+2 w) * (20 + 2 w) - 30 * 20 
        = 600 + 100 w + 4 w² - 600
    26 = 25 w + w²
    So  w = 1 m.
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kvnmurty: :-)
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