Question

Laura has a backyard that she wants to renovate. Her

backyard is (x + 4) feet wide and (x + 6) feet long.
Laura wants to place a rectangular garden that is x
feet wide and (x + 2) feet long in the middle of her
backyard. Laura also wants to pour in concrete that
surrounds her garden in the backyard that will serve
as a walkway. What is the expression that represents
the area of the walkway? Refer to the diagram.

Answer 1

Area of the walkway = 8x + 24

Explanation:

Area of the total backyard =
`l* b`

Area of total backyard =
`(x+6)* (x+4) = x^(2) +10x + 24`

Now, Area of the rectangular garden =
`l* b`

Area of the rectangular garden =
`x (x+2) = x^(2) + 2x`

Now area of the walkway poured with concrete = Area of the backyard - Area of the rectangular garden

=
`(x^(2) +10x +24) - (x^(2) +2x)`

=
`x^(2) + 10x +24 - x^(2) -2x`

= 8x + 24