Question 1189225
.
A pool is twice as long as it is wide and is surrounded by a walkway of uniform width of 1 foot. 
The combined area of the pool and the walkway is 400 square feet.
Find the dimensions of the pool and the area of the pool.
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            The starting equation, its solution and the answer all are incorrect in the post by @josgarithmetic.


            I came to bring a correct solution.



<pre>
Dimensions of the pool, 2x and x
Pool upper surface's area, 2x^2


Dimensions for the OUTER part of bordering walkway , 2x+2 and x+2


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The combined area of the pool and the walkway is 400 square feet.
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    (2x+2)(x+2) = 400

    ( x+1)*(x+2) = 200

    x^2+3x+2 = 200

    x^2 + 3x - 198 = 0


    x = {{{(-3+sqrt(9+4*198))/2}}}

    x = {{{(-3+sqrt(801))/2}}}

    x = {{{(-3+28.30194)/2}}}

    x = 12.651--------the width

    2*12.651 = 25.30-------the length


<U>CHECK</U>.  (25.30+2)*(12.651+2) = 400 square feet.


<U>ANSWER</U>.  The dimensions of the pool are 12.651 ft and 25.30 ft.

         The area of the pool is 12.651*25.30 = 320 square feet.
</pre>

Solved.


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To see many other similar solved problems, &nbsp;look into 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>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Surface-area/Cynthia-Besch-and-the-rug.lesson>Cynthia Besch wants to buy a rug for a room</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, &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.