Question

The camp athletic director wants to arrange kickball games for high school students and middle school students. Because of the ages of the campers, the high school kickball field is larger than the middle school field. The length of the square base path of the high school field is represented by the expression 2x−3 and the length of the middle school base path is represented by the expression x−8.

What is the area of the middle school field if its side measures x−8 feet?

What is the area of the high school field if its side measures 2x−3 feet?

Answer 1

Explanation:

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