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Below I will explain you on how to set up an equation to this problem.
The area of the large rectangle (the garden plus the walkway around the garden) is (2x+6)*(2x+10) square feet.
The area of the garden itself is 6*10 = 60 square feet.
The area of the walkway is the difference (2x+6)*(2x+10) - 60 square feet.
The volume of 1 cubic yards, converted to cubic feet is = 27 cubic feet.
When laid on the level ground with the thickness of 3 inches = of a foot,
1 cubic yard covers the area = 27*4 = 108 square feet.
So, 108 square feet is the area, which should be in the right side of this equation
(2x+6)*(2x+10) - 60 = 108.
Both sides of this equation represent the same quantity: the area of the walkway.
It leads to the equation
(2x +6)*(2x+10) = 168.
It is exactly the equation you asked about.
In the original solution under this link
https://www.algebra.com/algebra/homework/word/geometry/Geometry_Word_Problems.faq.question.1126574.html
the tutor obtained the same equation in another way (as the area of the large rectangle "the garden + the walkway").
After completing the setup, the solution goes on the way
shown by the tutor under the cited link.
To see many similar solved problems, see the lessons
- Problems on the area and the dimensions of a rectangle surrounded by a strip
- Cynthia Besch wants to buy a rug for a room
- Making a box from a piece of cardboard
- Problems on a circular pool and a walkway around it
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic
"Dimensions and the area of rectangles and circles and their elements".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.