SOLUTION: 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&

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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 20+2x
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
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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%28cross%2820%2B2x%29%29 (28+2x).
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          Notice that your writing was not exactly correct, so I fixed it . . .

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  x = 9.

Answer.   The path width is  9  meters.

Check.     Check it on your own.


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To see other similar solved problems, see 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".

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.