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15 April, 23:18

A school wants to have a metal gate placed around it. However they only want to cover three sides of the school and they only have 2000 feet of gate. What are the dimensions of the school if the area is 240,000 square feet?

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  1. 15 April, 23:46
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    Width = 139.445 ft and Length = 1721.11 ft or

    Width = 860.555 ft and Length = 278.89 ft

    Step-by-step explanation:

    If the school has a rectangular shape, we have that its perimeter and area are:

    Perimeter = 2*Length + 2*Width

    Area = Length * Width

    If we just want to cover 3 sides of the school, we can affirm that:

    2000 = Length + 2*Width (eq1)

    And the area is 240,000 ft2, so:

    240000 = Length * Width (eq2)

    From (eq1), we have that:

    Length = 2000 - 2*Width

    Using this value in (eq2), we have:

    240000 = (2000 - 2*Width) * Width

    240000 = 2000*Width - 2*Width^2

    Width^2 - 1000*Width + 120000 = 0

    Using Bhaskara's formula, we have:

    Delta = 1000^2 - 120000*4 = 520000

    sqrt (Delta) = 721.11

    Width1 = (1000 + 721.11) / 2 = 860.555 ft

    Width2 = (1000 - 721.11) / 2 = 139.445 ft

    If we use Width = 139.445 ft, we will find Length = 1721.11 ft

    If we use Width = 860.555 ft, we will find Length = 278.89 ft

    Both pairs of dimensions are valid answers, as they would use 2000 feet of gate and the area of the school would be 240,000 ft2
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