Answer:
An expression for the area of the pathway is [tex]4x^2+42x[/tex]
Step-by-step explanation:
Length of garden = 9 feet
Breadth of garden = 12 feet
Area of garden = [tex]Length \times Breadth = 9 \times 12 =108 ft^2[/tex]
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 =[tex]Length \times Breadth = (9+2x)(12+2x)[/tex]
Area of path = Area of path including garden - Area of garden
Area of path =[tex](9+2x)(12+2x)-108[/tex]
Area of path =[tex]108+18x+24x+4x^2-108[/tex]
Area of path =[tex]4x^2+42x[/tex]
Hence an expression for the area of the pathway is [tex]4x^2+42x[/tex]
