Question

You are planning a rectangular dining pavilion. Its length is three times its width x. You want a stone walkway that is 3 ft wide around the pavilion. You have enough stones to cover 396 ft^2 and want to use them all in the walkway. What should the dimensions of the pavilion be? How can you write a variable expression for the area of the walkway?

Answer 1

The dimensions of the pavilion are:

y=length= 45 ft.

x= width= 15 ft.

And the varable expression for the area of the walkaway is:

`A_w=36+24x`

Explanation:

1. Let be y= length and x= width of the dining pavilion.

2. Then we have that y=3x and the dining´s area is:

`A_D= length*width\\A_D=3x*x=3x^(2) \\`

3. The walkway is 3ft wide around the pavilion, it means that its area will be:

`A_w=length*width\\ A_w=(6+3x)*(6+x)\\A_w=36+6x+18x+3x^2-3x^2\\A_w=36+24x`

Where
`w=36+24x` is a variable expression for the area of the walkaway.

4. We have that the total area to cover for the stones is 396 ft^2 then matching:

[tex]396=36+24x\\396-36=24x\\360=24x\\x=\frac{360}{24}\\ x=15 ft (wide of the pavilion)\\ y=3x\\y=3*15\\y=45 ft.

And y=length of the pavilion