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22 March, 04:05

Suppose the carnival director asks you to create a game board that is 1,120 square inches. Find the dimensions that would meet this request by setting the area equation equal to 1,120, solving for x, and substituting x into the expressions for the length and width.

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  1. 22 March, 04:09
    0
    Factor of 1,120 are

    =2 * 2 * 2 * 2 * 2 * 5 * 7

    So, we have to find dimensions of Length and Breadth, such that area of game board is 1,120 square inches.

    There are many possible dimensions.

    We will find the dimension of card board in terms of natural numbers such that difference between Length and breadth is Least.

    One of the Possible Dimension can be

    Length = 7 * 5=35 inches

    Breadth=2*2*2*2*2=32 inches

    Other Possible dimension can be

    Length=5*2*2*2=40

    Breadth=7*2*2=28

    So, selecting those dimension in which difference between Length and Breadth is Least

    Length = 35 inches

    Breadth=32 inch

    Expressing it in terms of, x

    →Let, Breadth = x inches

    →Length = (x+3) inches

    ⇒Area of Square board which is in the shape of rectangle = Length * Breadth

    → 1120=x * (x+3)

    Using Distributive property

    →x²+3x=1120

    →x²+3x-1120=0
  2. 22 March, 04:31
    0
    length x width = (56 ft) x (20 ft) = 1120 sq. ft.
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