Question 1050788
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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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<pre><b>
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 + 56x + 34x + 4x^2}}} - 28*17 = 144,

{{{4x^2 + 90x}}} = 144,

{{{4x^2 + 90x - 144}}} = {{{0}}}.

Apply the quadratic formula

{{{x[1,2]}}} = {{{(-90 +- sqrt(90^2-4*4*(-144)))/(2*4)}}} = {{{(-90 +- 102)/8}}}.

Ignore the negative root. Then you have an unique solution  x = {{{12/8}}} =  {{{1}}} {{{1/2}}} ft = 1.5 ft.

<U>Answer</U>.  The walkway width is 1.5 ft.
</pre>

For more similar solved problems see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Surface-area/Problems-on-the-area-of-a-rectangle-surrounded-by-a-strip.lesson>Problems on the area and the dimensions of a rectangle surrounded by a strip</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Surface-area/Circular-pool-and-a-walkway-around.lesson>Problems on a circular pool and a walkway around it</A>

in this site.


Also, you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the parts of this textbook in the chapter "<U>Dimensions and the area of rectangles and circles and their elements</U>".