Question

The length of a rectangular garden ABCD is 9 feet more than its width. It is surrounded by a brick walkway 4 feet wide as shown below. Suppose the total area of the walkway is 400 square feet. What are the dimensions of the garden?

PLEASE HELP I KEEP TRYING TO DO IT BUT IT DOESN'T WORK.

Answer 1

The dimensions of the garden are

Length
`25.5\ ft` and Width
`16.5\ ft`

Explanation:

Let

x----> the length of the rectangular garden

y ---> the width of the rectangular garden

Aw ----> the area of the walkway

we know that

`x=y+9` ----> equation A

`Aw=(x+8)(y+8)-xy`

`Aw=400\ ft^(2)`

so

`400=(x+8)(y+8)-xy\\400=xy+8x+8y+64-xy`

`400=8x+8y+64` ----> equation B

Substitute equation A in equation B

`400=8(y+9)+8y+64`

`400=8y+72+8y+64`

`400=16y+136`

`16y=400-136`

`y=16.5\ ft`

Find the value of x

`x=16.5+9=25.5\ ft`

therefore

The dimensions of the garden are

Length
`25.5\ ft`

Width
`16.5\ ft`