We know that
• The dimensions of the pool are 26 meters by 12 meters.
,
• The uniform surrounding path has a width of ,x, meters.
To find a function of x to express the whole area, we have to define the width and length including the path.
The width would be-
[tex]w=26-2x[/tex]
The length is
[tex]l=12+2x[/tex]
The total area is
[tex]\begin{gathered} A=w\cdot l \\ A(x)=(26-2x)(12+2x) \end{gathered}[/tex]
We use the distributive property to show the function in the simplest form.
[tex]A(x)=312+52x-24x-4x^2[/tex]
Then, we reduce like terms. So, the function is
[tex]A(x)=-4x^2+28x+312[/tex]
