Question

The length of a rectangular park is twice it's width. The park is surrounded by a 3-foot-wide path. Let x denote the width of the park. Write a quadratic function to represent the total area of the park and the path.

Answer 1

Answer:

The quadratic function  representing the total area of the park and the path is $2x^2 + 27x +81$

Step-by-step explanation:

The width of the rectangle is x----------(1)

Then the length  =  twice it's width

Length =  $2 \times width$

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 = $Length \times width$

that is

=>  (2x + 9)(x+9)

=>$2x^2 + 18x +9x +81$

=> $2x^2 + 27x +81$