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A rectangular garden of length 28 ft and width 17 ft is surrounded by a path of uniform width.
If the area of the walkway is 144 ft2, what is its width?
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The larger rectangle has the dimensions (28+2x) and (17+2x), where x is the uniform width of the walkway, in feet.
The smaller rectangle (the garden) has the area of 28*17 square feet.
You are given the difference
(28+2x)*(17+2x) - 28*17 = 144.
Simplify this equation
- 28*17 = 144,
= 144,
= .
Apply the quadratic formula
= = .
Ignore the negative root. Then you have an unique solution x = = ft = 1.5 ft.
Answer. The walkway width is 1.5 ft.
For more similar solved problems see the lessons
- Problems on the area and the dimensions of a rectangle surrounded by a strip
- 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 parts of this textbook in the chapter "Dimensions and the area of rectangles and circles and their elements".