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Let W be the uniform width, in meters.
The the dimensions of the backyard are (11+2W) and (8+2W), and its area is
(11+2W)*(8+2W) = 460.
You can solve it by applying the quadratic formula to quadratic equation.
Or mentally, by finding decomposition of the number 460 into the product of two factors with the difference of 11-8 = 3 between them:
460 = 20*23.
The width then is 8+2W = 20 ====> 2W = 20-8 = 12 ====> W = 12/2 = 6 meters.
Answer. The uniform width of the strip around the pool is 6 meters.
Solved.
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To see many other similar solved problems, look into the lesson
- Problems on the area and the dimensions of a rectangle surrounded by a strip
- Cynthia Besch wants to buy a rug for a room
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.