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3 February, 02:36

City purchases a square plot of land with an area of (x2 + 24x + 144) square yards for a park. The dimensions of the plot are of the form ax + b, where a and b are whole numbers. Find an expression in terms of x for the perimeter of the park. An expression in terms of x for the perimeter of the park is Select ... select 8) The perimeter of the park when x = 10 yards

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  1. 3 February, 06:05
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    Area has been given as (x² + 24x + 144)

    when we factorise this quadratic formula

    (x² + 24x + 144)

    = x² + 12x + 12x + 144

    = x (x + 12) + 12 (x + 12)

    (x+12) (x+12)

    the area of the square plot has been calculated by multiplying the lengths of the 2 sides. As its a square, all sides are equal

    the length of one side = x+12

    the dimensions are given in the form ax + b

    from the length x + 12, a = 1 and b=12

    the perimeter of the park = 4 * length of one side

    therefore perimeter = 4 * (x+12)

    = 4x + 48 yards

    next we are asked to find the perimeter when x = 10 yards

    perimeter = 4*10 + 48 = 40 + 48 = 88 yards
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