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Math Help - Word problem

  1. #1
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    Question Word problem

    Q) A rectangular field , 70m long and 50m wide, has a path of uniform width around it .If the area of the path is 1024m^2 , find the width of the path.

    Solution let x be the uniform width of the path

    According to the given condition,

    (50+2x)(70+2x)-1024=50*70

    ...............................

    and the answer comes out to be 4m after solving this.


    I have problem in that how the bold equation is formed ?
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  2. #2
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    e^(i*pi)'s Avatar
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    You know the area of a rectangle to be A = lw and so A_{f} = 50 \times 70 \text{ m}^2

    Like they did, let x be the width of the path.

    Now consider the length of the field and path - it is going to be the length of the field (70) plus the width of the path at both ends (2x) which is equal to l = 70+2x
    Do the same for the width and the path: w = 50+2x

    The area of the field+path is also length x width: A_{f+p} = (50+2x)(70+2x)

    The area of the path will be the area of the field+path minus the area of the filed: A_p = A_{p+f} - A_f - you are given that A_p = 1024 and so the equation is 1024 = (50+2x)(70+2x) - 50 \times 70


    Which can be rearranged into (50+2x)(70+2x) - 1024 = 50 \times 70
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