The NFL has contacted you to design its new stadium, they wanted to leave a square room for vendors in each corner. Service provided you a 20-in by 30-in rectangular piece of cardboard to create a miniature model. The area of the field (not including the portion sectioned off for vendors and r bleachers) is to be 375 square inches. What is the length of the side of the square area that is assigned for vendors?

If I was provided with a 20 inch by 30 inch rectangular piece of cardboard paper; in order to calculate the area of this rectangular piece, we would state the formula for finding the area of a rectangle = L × W.

Here, the length of the rectangle is 30 inches while the width of the rectangle is 20 inches. The total area of this rectangle is then:-

30 inches × 20 inches = 600 square inches.

Now, we were also told that every corner in the stadium must have a portion that is sectioned off for vendors. Since there are four rectangles in a rectangle/stadium, there would be four portions in the cardboard paper that will be carved out for vendors and each of these portions will be a square.

Again, the area of the field/rectangle that does not include the sectioned off portion is 375 square foot. To calculate the total areas of the portions that will be carved out for vendors, we will subtract the area of the field that doesn't include the portions for vendors from the total area of the field/rectangle.

That is: 600 square inches - 375 square inches = 225 square inches.

So, if every corner of the field must have a portion carved out for vendors, then the total number of portions that will be carved out for vendors is four(4). Therefore, the sum of the separate "areas" of these four portions will give 225 square inches.

To find the area of one of these portions, we will divide the sum of the areas of the four portions by 4.

= 225/4

= 56.25 square inches

The area of one of the four portions that must be carved out for vendors in the field/rectangular cardboard piece is 56.25 square inches

Recall that each portion must be a square. To find the length of one side of each square, we need the formula for calculating the area of a square =

L × L = A

Where, A is the area of one of the squares (56.25 square inches)

L is the length of one square ( the unknown term).

Substituting appropriately:-

L × L = 56.25

[tex]L^{2}[/tex] = 56.25

L = [tex]\sqrt{56.25}[/tex]

L = 7.5 inches or [tex]7\frac{1}{2}[/tex] inches.

Therefore, the length of a side of each of the four square portions carved out for vendors is 7.5 inches or [tex]7\frac{1}{2}[/tex] inches.