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

Answer:

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

Step-by-step explanation:

Length of garden = 9 feet

Breadth of garden = 12 feet

Area of garden = $Length \times Breadth = 9 \times 12 =108 ft^2$

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 =$Length \times Breadth = (9+2x)(12+2x)$

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 $4x^2+42x$