Question

Have have a garden that is 9 feet by 12 feet and you want to buy a pathway around the garden that is x feet, write an expression for the area of the pathway

Answer 1

An expression for the area of the pathway is
`4x^2+42x`

Explanation:

Length of garden = 9 feet

Breadth of garden = 12 feet

Area of garden =
`Length * Breadth = 9 * 12 =108 ft^2`

We are given that you want to buy a pathway around the garden that is x feet

Width of pathway = x feet

Outer length = 9+x+x=9+2x

Outer breadth = 12+x+x=12+2x

Area of path including garden =
`Length * Breadth = (9+2x)(12+2x)`

Area of path = Area of path including garden - Area of garden

Area of path =
`(9+2x)(12+2x)-108`

Area of path =
`108+18x+24x+4x^2-108`

Area of path =
`4x^2+42x`

Hence an expression for the area of the pathway is
`4x^2+42x`