A camp athletic director wants to arrange kickball games for highschool and middle school students. Because of the age of the campers, the highschool kickball field is larger than the middle school field. The dimensions of the square base paths are

Highschool = 2x-3 ft

Middle school = x-8 ft

What is the area of the high school field's base path?

What is the area of the middle school field's base path?

What is the difference in size of the two field's base path?

The area of the high school field's base path is (4x^2 - 12x + 9) ft^2

The area of the middle school field's base path is (x^2 - 16x + 64) ft^2

The difference in size between the two is

(3x^2 + 4x - 55) ft^2

Step-by-step explanation:

Firstly, we are to calculate the area of the high school field's base path

Mathematically, the area of a square is L^2

where L is the length of the side of the square. The area of the high school field base path is thus;

(2x-3) * (2x-3) = 2x (2x-3) - 3 (2x-3) = 4x^2 - 6x - 6x + 9 = (4x^2 - 12x + 9) ft^2

The area of the middle school field's base path can be calculated in a similar fashion

That would be (x-8) * (x-8) = x (x-8) - 8 (x-8) = x^2 - 8x - 8x + 64 = (x^2 - 16x + 64) ft^2

The difference in size between this two will be;

(4x^2 - 12x + 9) - (x^2 - 16x + 64) = 4x^2-x^2-12x+16x+9-64 = (3x^2 + 4x - 55) ft^2