Question

assume a pool measuring 26 meters by 12 meters is surrounded by a path of uniform width as shown in the figure Express the area in the past A in Square meters as a function of its width X in meters

Answer 1

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-

`w=26-2x`

The length is

`l=12+2x`

The total area is

`\begin{gathered} A=w\cdot l \\ A(x)=(26-2x)(12+2x) \end{gathered}`

We use the distributive property to show the function in the simplest form.

`A(x)=312+52x-24x-4x^2`

Then, we reduce like terms. So, the function is

`A(x)=-4x^2+28x+312`