Answer:
The quadratic function representing the total area of the park and the path is [tex]2x^2 + 27x +81[/tex]
Step-by-step explanation:
The width of the rectangle is x----------(1)
Then the length = twice it's width
Length = [tex]2 \times width[/tex]
Length = 2x------------------(2)
Now the width along with the foot path = x +3+3 = x+9
the length along with the foot path = 2x + 3+3 = 2x +9
The total area of the park and the path = [tex]Length \times width[/tex]
that is
=> (2x + 9)(x+9)
=>[tex]2x^2 + 18x +9x +81[/tex]
=> [tex]2x^2 + 27x +81[/tex]
The area of the rectangular park is expressed as [tex]a = x^2 + 6x + 9[/tex]
Data;
The area of a rectangle is the product of it's length and width.
[tex]A = l * w[/tex]
Let's substitute the values into the equation
[tex]A = l * w\\A = 2(x + 3) * (x + 3)\\A = (2x + 6) * (x + 3)\\A = 2x^2 + 6x + 6x + 18\\A = 2x^2 + 12x + 18\\A = x^2 + 6x + 9[/tex]
The area of the rectangular park is expressed as [tex]a = x^2 + 6x + 9[/tex]
Learn more on area of a rectangle here;
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