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.

length x width = (56 ft) x (20 ft) = 1120 sq. ft.

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