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10 January, 01:24

The area of a rectangular park is 4 mi^2. The park has a width that is equal to "w", and a length that is 3 mi longer than the width of the park. Find the dimensions of the park.

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  1. 10 January, 01:51
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    l = 4 mi : width of the park

    w = 1 mi : length of the park

    Explanation:

    Formula to find the area of the rectangle:

    A = w*l Formula (1)

    Where,

    A is the area of the rectangle in mi²

    w is the width of the rectangle in mi

    l is the width of the rectangle in mi

    Known data

    A = 4 mi²

    l = (w+3) mi Equation (1)

    Problem development

    We replace the data in the formula (1)

    A = w*l

    4 = w * (w+3)

    4 = w²+3w

    w²+3w-4 = 0

    We factor the equation:

    We look for two numbers whose sum is 3 and whose multiplication is - 4

    (w-1) (w+4) = 0 Equation (2)

    The values of w for which the equation (2) is zero are:

    w = 1 and w = - 4

    We take the positive value w = 1 because w is a dimension and cannot be negative.

    w = 1 mi : width of the park

    We replace w = 1 mi in the equation (1) to calculate the length of the park:

    l = (w+3) mi

    l = (1+3) mi

    l = 4 mi
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