Question

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)

Answer 1

Answer:

a) The polynomial is equivalent to $A = (x-15)^{2}$, and the side length of the playground is $x -15$ feet.

b) The perimeter of the playground, measured in feet, is $p = 4\cdot (x-15)$.

Step-by-step explanation:

a) By Geometry, we know that area of the square is equal to the square of the side length. If $A = x^{2}-30\cdot x +225$ is the area of the square, then must be a perfect square trinomial, that is:

$(x-a)^{2} = x^{2}-2\cdot a\cdot x + a^{2}$ (1)

Then, we must observe the following properties:

$-2\cdot a = -30$ (2)

$a = 15$

$a^{2} = 225$ (3)

$a = 15$

Therefore, the polynomial is equivalent to $A = (x-15)^{2}$, and the side length of the playground is $x -15$ feet.

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

$p = 4\cdot (x-15)$

The perimeter of the playground, measured in feet, is $p = 4\cdot (x-15)$.