A= x^2 -30x+225 The polynomial represents the area (in square feet) of the square playground. a. Write a polynomial that represents the side length of the playground. b. Write an expression for the perimeter of the playground. (I factored it and got (x-15)^2)

a) The polynomial is equivalent to , and the side length of the playground is feet.

b) The perimeter of the playground, measured in feet, is .

Step-by-step explanation:

a) By Geometry, we know that area of the square is equal to the square of the side length. If is the area of the square, then must be a perfect square trinomial, that is:

(1)

Then, we must observe the following properties:

(2)

(3)

Therefore, the polynomial is equivalent to , and the side length of the playground is feet.

b) The perimeter of a square equals four times the side length. That is:

The perimeter of the playground, measured in feet, is .

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50