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

Answer:

Area of the walkway = 8x + 24

Step-by-step explanation:

Area of the total backyard = $l\times b$

Area of total backyard = $(x+6)\times (x+4) = x^{2} +10x + 24$

Now, Area of the rectangular garden = $l\times b$

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