Question 1107364
.
A pool measuring 
20 meters by 
28 meters is surrounded by a path of uniform​ width, as shown in the figure. If the area of the pool and the path combined is 
1748 square​ meters, what is the width of the​ path? The width of the outside the sidewalk is 20+2x by {{{highlight(cross(20+2x))}}} (28+2x).
~~~~~~~~~~~~~~~~~~~~~~


<pre>
          Notice that your writing was not exactly correct, so I fixed it . . . 
</pre>

Based on all the array of info (data + hint/instruction + my correction) your equation is


(20+2x)*(28+2x) = 1748.


Simplify and solve this quadratic equation.


560 + 56x + 40x + 4x^2 = 1748

4x^2 + 96x -1748 + 560 = 0

4x^2 + 96x - 1188 = 0

x^2 + 24x - 297 = 0

(x+33)*(x-9) = 0.


The only positive solution is &nbsp;x = 9.
</pre>

<U>Answer</U>.  &nbsp;&nbsp;The path width is &nbsp;9&nbsp; meters.


<U>Check</U>.   &nbsp;&nbsp;&nbsp;&nbsp;Check it on your own.



-----------------
To see other similar solved problems, see the lesson

&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>

in this site.



Also, &nbsp;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 lesson is the part of this online textbook under the topic 
"<U>Dimensions and the area of rectangles and circles and their elements</U>".


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.