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Let x be that unknown width, in feet.
The area of the pool is 19*13 sq. ft.
The exterior dimensions of the larger rectangle are (19+2x) ft and (13+2x) ft.
Hence, the area of the larger rectangle is the product (19+2x)*(13+2x) sq. ft.
Then the area of the walkway around the pool is the difference (19+2x)*(13+2x) - 19*13.
So, your equation expressing this area is
(19+2x)*(13+2x) - 19*13 = 273.
Solve it and find x.
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To see more samples/examples of solved problems of this type, look into the lesson
- Problems on the area and the dimensions of a rectangle surrounded by a strip
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 lesson is the part of this online textbook under the topic
"Dimensions and the area of rectangles and circles and their elements".